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Algebra 1 : Functions and Lines

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Example Question #3351 : Algebra 1

What is the inverse of the function defined by the following set of ordered pairs?

$\left \{ (1,9), (2,8), (3,7), (4,6), (5,5) \right \}$

Possible Answers:

$\left \{ (-1,-9), (-2,-8), (-3,-7), (-4,-6), (-5,-5) \right \}$

The function does not have an inverse.

$\left \{ (1,-9), (2,-8), (3,-7), (4,-6), (5,-5) \right \}$

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

$\left \{ \left(1,\frac{1}{9} \right ), \left(2,\frac{1}{8} \right ), \left(3,\frac{1}{7} \right ), \left(4,\frac{1}{6} \right ), \left(5,\frac{1}{5} \right ) \right \}$

Correct answer:

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$

Explanation:

The inverse of a function is the relation that switches the positions of the coordinates of each ordered pair. Therefore, the correct choice is

$\left \{ (9,1), (8,2), (7,3), (6,4), (5,5) \right \}$ .

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Example Question #23 : Algebraic Functions

Find the inverse of this function.

$y=\frac{x}{x-3}$

Possible Answers:

$y=\frac{-3x^{2}}{1-x^{2}}$

$y=\frac{3x}{1-x}$

$y=\frac{-3x}{1-x}$

$y=\frac{-3x}{1+x}$

No inverse exists

Correct answer:

$y=\frac{-3x}{1-x}$

Explanation:

The inverse of an equation is given by solving for the x value in terms of y. To find the inverse, take the original equation, $y=\frac{x}{x-3}$ , and solve for x.

First multiply both sides by (x – 3).

y(x-3)=x

Distribute y into the parenthesis.

xy-3y=x

Subtract xy to both sides.

-3y=x-xy

Factor the x.

-3y=x(1-y)

Divide both sides by (1 – y).

$x=\frac{-3y}{1-y}$

Once you have solved for x, switch the x and y terms.

$y=\frac{-3x}{1-x}$

Though an inverse function is found by solving for x, it still must follow the "y=" convention.

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Example Question #24 : Algebraic Functions

Given $f{\left (x \right )}= x^{2} - 5, g\left ( x \right ) = 2x -3$

Find $f\cdot g\left ( x \right )\ OR\ f( g\left ( x \right ))$ .

Possible Answers:

2x-8

$4x^{2}+4$

$x^{2}+2x -8$

$4x^{2}-6x +5$

$4x^{2}-12x + 4$

Correct answer:

$4x^{2}-12x + 4$

Explanation:

$f\left ( x \right ) = x^{2} -5$

Replacing or substituting g(x) for in $f\left ( x \right )$ we get $f(g\left ( x \right ))=$

$\left ( 2x-3 \right )^{2}-5$

When simplified we get

$4x^{2}-12x +4$

which is the correct answer.

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Example Question #25 : Algebraic Functions

Given $f\left ( x \right ) = x^{2}-5\ and\ g(x) = 2x-3$

Find $g\bullet f\left ( x \right ) = g\left ( f\left ( x \right ) \right )$ .

Possible Answers:

$x^{2}+2x -8$

$2x^{2}-10$

$2x^{2} - 13$

$\left ( 2x-3 \right )^{2}$

$4x^{2}-12x+4$

Correct answer:

$2x^{2} - 13$

Explanation:

$g\left ( f\left ( x \right ) \right ) = 2\left ( x^{2} \right - 5) -3$

which is equal to

$2x^{2} - 13$

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Example Question #26 : Algebraic Functions

Given $f\left ( x \right ) = x^{2} - 5$ .

Find $f\left ( f\left ( x \right ) \right )$ .

Possible Answers:

$x^{4} - 10x^{2} + 20$

$\left (x^{2} - 5\right )^{2}$

$x^{2} - 10$

$\left ( x^{2}\ - 5)^{4}$

$x^{2} - 5$

Correct answer:

$x^{4} - 10x^{2} + 20$

Explanation:

Given $f\left ( x \right )$ = $x^{2}- 5$

Replacing in the above equation with $f\left ( x \right )$

one gets $\left ( x^{2} - 5\right )^{2} -5$

Upon simplification one gets the correct answer which is

$x^{4}-10x^{2} + 20$

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Example Question #27 : Algebraic Functions

Given $g\left ( x \right ) = 2x-5$

Find $g\left ( g\left ( x \right ) \right )$ .

Possible Answers:

$\left (2x-5 \right )^{2}$

4x-15

$4x^{}2 + 25$

2x-5

$4x^{2} -25$

Correct answer:

4x-15

Explanation:

$g\left ( x \right ) = 2x-5$

Substituting g(x) in place of above equation one gets the following:

$2\left ( 2x-5 \right ) - 5$

which, after simplification, gives us the correct answer which is

4x-15

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Example Question #28 : Algebraic Functions

Given $f\left ( x \right ) = -x^{2} -3$

and $g\left ( x \right ) = 2x+3$

Find $f\left ( -2 \right ) - g\left ( -2 \right )$

Possible Answers:

Correct answer:

Explanation:

$f\left ( -2 \right ) - g\left ( -2 \right ) = \left [-\left ( -2 \right )^{2} - 3 \right ] - \left [ 2\left ( -2 \right ) +3\right ]$

=-4-3-(-4+3)

=-7-(-1)

=-7+1

=-6

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Example Question #1 : Mean

There exists a function f(x) = 3x + 2 for x = 2, 3, 4, 5, and 6. What is the average value of the function?

Possible Answers:

Correct answer:

Explanation:

First we need to find the values of the function: f(2) = 3 * 2 + 2 = 8, f(3) = 11, f(4) = 14, f(5) = 17, and f(6) = 20. Then we can take the average of the five numbers:

average = (8 + 11 + 14 + 17 + 20) / 5 = 14

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Example Question #1 : Function Notation

Solve the function for . When f(x)=16

What does equal when, f(x)=16

$f(x)=x^{2}-9$

Possible Answers:

$\sqrt{5}$

$\pm5$

-5

Correct answer:

$\pm5$

Explanation:

Plug 16 in for f(x) . 16=x^2-9

Add 9 to both sides. x^2=25

Take the square root of both sides. $\sqrt{25}$ = $\sqrt{x^{2}}$

Final answer is $\pm5$

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Example Question #71 : Functions And Lines

Define $f (x) = 3 - \sqrt{x-1}$ and $g\left ( x\right ) = 3 + \sqrt{x-1}$ .

Evaluate $\left (f-g \right ) (17)$ .

Possible Answers:

$\left (f-g \right ) (17)$ is undefined.

Correct answer:

Explanation:

First evaluate f (17) and g(17) , then subtract.

$f (x) = 3 - \sqrt{x-1}$

$f (17) = 3 - \sqrt{17-1} = 3 - \sqrt{16} = 3-4 = -1$

$g\left ( x\right ) = 3 + \sqrt{x-1}$

$g(17) = 3 + \sqrt{17-1} = 3 + \sqrt{16} = 3+4 = 7$

$\left (f-g \right ) (17) = f(17)-g(17) = -1-7 = -8$

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3351 : Algebra 1

Example Question #23 : Algebraic Functions

Example Question #24 : Algebraic Functions

Example Question #25 : Algebraic Functions

Example Question #26 : Algebraic Functions

Example Question #27 : Algebraic Functions

Example Question #28 : Algebraic Functions

Example Question #1 : Mean

Example Question #1 : Function Notation

Example Question #71 : Functions And Lines

All Algebra 1 Resources

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