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SAT Math : How to find f(x)

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Example Question #91 : How To Find F(X)

Two functions

Define and to be the functions graphed above. Evaluate

$\left (g^{-1} \circ f \right ) (5)$ .

Possible Answers:

The expression is not defined.

$\left (g^{-1} \circ f \right ) (5) = -5$

$\left (g^{-1} \circ f \right ) (5) = -4$

$\left (g^{-1} \circ f \right ) (5) = -3$

$\left (g^{-1} \circ f \right ) (5) = 1$

Correct answer:

The expression is not defined.

Explanation:

It can be seen below that a horizontal line can be drawn through two points of the graph of .

Hlt

fails the Horizontal Line Test, which means that has no inverse. $g^{-1}$ does not exist, so the expression $\left (g^{-1} \circ f \right ) (5)$ is undefined.

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Example Question #92 : How To Find F(X)

Function 4

Define as the function graphed above. Define function g (x) = 3x - 5 .

Evaluate $\left (g \circ f \right ) (3)$ .

Possible Answers:

3 is not in the domain of $g \circ f$ .

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -2 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -2$

$\left (g \circ f \right ) (3) = 4$

Correct answer:

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

Explanation:

$\left (g \circ f \right ) (3) = g \left [ f (3)\right ]$ .

As can be seen in the diagram below, $f(3) = -2\frac{1}{2} = -\frac{5}{2}$ . Function 4a

Therefore,

$\left (g \circ f \right ) (3) = g \left ( - \frac{5}{2}\right )$

g (x) = 3x - 5 , so

$g \left ( - \frac{5}{2}\right ) = 3\left ( - \frac{5}{2}\right ) -5$

$= - \frac{15}{2} -5$

$= - 7 \frac{1}{2}-5$

$= -12\frac{1}{2}$

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Example Question #93 : How To Find F(X)

Two functions

Define and to be the functions graphed above.

Evaluate $(f \circ g ) (4)$

Possible Answers:

4 is not in the domain of $f \circ g$ .

$\left (f \circ g \right ) (4) = -2$

$\left (f \circ g \right ) (4) = -3$

$\left (f \circ g \right ) (4) = -6$

$\left (f \circ g \right ) (4) = -3 \frac{1}{6}$

Correct answer:

$\left (f \circ g \right ) (4) = -2$

Explanation:

$\left (f \circ g \right ) (4) = f \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f \circ g \right ) (4) = f (-4)$ .

From the diagram below, it can be seen that

f(-4) = -2 .

Two functions f

Therefore, the correct response is that $\left (f \circ g \right ) (4) = -2$ .

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Example Question #94 : How To Find F(X)

Two functions

Define and to be the functions graphed above. Evaluate

$\left (f^{-1} \circ g \right ) (4)$

Possible Answers:

$\left (f ^{-1} \circ g \right ) (4) = -1$

$\left (f ^{-1} \circ g \right ) (4) = -20$

$\left (f ^{-1} \circ g \right ) (4) = 2$

$\left (f^{-1} \circ g \right ) (4)$ is undefined.

$\left (f ^{-1} \circ g \right ) (4) = -8$

Correct answer:

$\left (f ^{-1} \circ g \right ) (4) = -8$

Explanation:

$\left (f ^{-1}\circ g \right ) (4) = f^{-1} \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f ^{-1} \circ g \right ) (4) = f^{-1} (-4)$ .

From the diagram below, it can be seen that

f(-8) = -4 .

Two functions f

so, by definition,

$f ^{-1} (-4)= -8$ .

Therefore, the correct response is that

$\left (f ^{-1} \circ g \right ) (4) = -8$ .

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Example Question #95 : How To Find F(X)

Function 4

Define as the function graphed above. Define function $g(x) = x^{2}- 11$ .

Evaluate $\left (f \circ g \right ) (4)$ .

Possible Answers:

$\left (f \circ g \right ) (4) = -7$

$\left (f \circ g \right ) (4) = -10$

$\left (f \circ g \right ) (4) = - \frac{1}{2}$

$\left (f \circ g \right ) (4) = -15$

4 is outside the domain of $f \circ g$

Correct answer:

$\left (f \circ g \right ) (4) = - \frac{1}{2}$

Explanation:

$\left (f \circ g \right ) (4) = f \left [ g (4)\right ]$

$g(x) = x^{2}- 11$ , so

$g(4) = 4^{2}- 11 = 16-11 = 5$

$\left (f \circ g \right ) (4) = f (5)$ .

From the diagram below, we see that $f(5) = -\frac{1}{2}$ .

Function 4a

The correct response is that $\left (f \circ g \right ) (4) = - \frac{1}{2}$ .

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Example Question #96 : How To Find F(X)

Two functions

Define and to be the functions graphed above. For which of the following values of is the statement

(f-g)(x) = 0

a true statement?

Possible Answers:

x= -1

The statement is not correct for any value of .

x= 0

x= -2

x=1

Correct answer:

x= 0

Explanation:

f(x) - g(x) = 0

f(x)= g(x)

This can be solved by graphing and on the same set of axes and noting their points of intersection:

Two functions together

The graphs of the two functions intersect at the point (0, 1) . Therefore,

f(0) = g(0) , and

(f-g)(0) = 0 .

The correct response is x= 0 .

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Example Question #97 : How To Find F(X)

Function 4

Define to be the function graphed above.

Which of the following is an -intercept of the graph of the function , if is defined as

g(x ) = f(x+ 5) ?

Possible Answers:

(-9, 0)

(-3, 0)

(-7, 0)

The graph of has no -intercept.

$\left ( -4\frac{1}{2}, 0 \right )$

Correct answer:

(-7, 0)

Explanation:

An -intercept of the graph of has as its -coordinate a value such that

g(x) = 0 ,

or, equivalently,

f(x+ 5) = 0

From the diagram, we can see that

$f(-8) = f(-2) = f \left ( 5 \frac{1}{2}\right ) = 0$

Therefore, to find the -intercepts of , set x+5 equal to these numbers; equivalently, subtract 5 from each number. We get that

$g(-13) = g(-7) = g \left ( \frac{1}{2} \right )= 0$

Therefore, the -intercepts of the graph of are the points

(-13, 0) , (-7, 0) , $\left ( \frac{1}{2}, 0 \right )$ .

The correct choice is (-7, 0) .

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Example Question #131 : Algebraic Functions

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(x-4) .

Possible Answers:

(0,4)

(0, -2)

(0,-8)

(0,0)

The graph of has no -intercept.

Correct answer:

(0,4)

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(x-4)

g(0) = f(0-4)= f( -4)

As can be seen in the diagram below, f( -4) = 4 .

Function 4a

Therefore, g(0) = 4 , and the correct response is (0,4) .

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Example Question #99 : How To Find F(X)

Define a function as follows:

$g (x) = x ^{2} - 8x + 17$ , where the domain of is the set [0, 9] .

Give the range of .

Possible Answers:

$[17, \infty )$

$[1 , \infty )$

[17, 26]

[1, 26]

[1, 17]

Correct answer:

[17, 26]

Explanation:

This problem can be solved by examining the behavior of the graph of $g (x) = x ^{2} - 8x + 17$ , which is a parabola.

Since the quadratic coefficient is 1, a positive number, its vertex is a minumum. The -coordinate of the vertex can be found by setting a = 1, b= -8 , and calculating:

$x = - \frac{b}{2a} = -\frac{-8}{2 \cdot 1} = 4$

The -coordinate is

$g (4) = 4 ^{2} - 8 (4) + 17 = 16 - 32 + 17 = 1$

The minimum value of is therefore 1, and this occurs at $x = 4 \in [0, 9]$ . This makes 1 the lower bound of the range.

Since the graph of is a parabola, it decreases everywhere for x < 4 and increases everywhere for x > 4 . Therefore, we can evaluate g(0) and g(9) , and choose the higher value as the maximum value on the given domain.

$g (0) = 0 ^{2} - 8 (0)+ 17 = 0 - 0 + 17 = 17$

$g (0) = 9 ^{2} - 8 (9)+ 17 = 81 - 72 + 17 = 26$

We choose 26 as the upper bound of the range.

Therefore, the range of , given the domain restriction, is the set [17, 26] .

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Example Question #100 : How To Find F(X)

$\frac{x-4}{x}=\frac{6}{18}$

Possible Answers:

Correct answer:

Explanation:

The first step is to cross multiple which leaves you with 18x-72=6x . The next step is to get all x's on one side of the equation and all constants on the other. You can add to both sides then subtract from both sides. This gives us 12x=72 . The last step is to get by itself by dividing each side by giving an answer of x=6

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SAT Math : How to find f(x)

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #91 : How To Find F(X)

Example Question #92 : How To Find F(X)

Example Question #93 : How To Find F(X)

Example Question #94 : How To Find F(X)

Example Question #95 : How To Find F(X)

Example Question #96 : How To Find F(X)

Example Question #97 : How To Find F(X)

Example Question #131 : Algebraic Functions

Example Question #99 : How To Find F(X)

Example Question #100 : How To Find F(X)

All SAT Math Resources

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