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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #671 : Algebra Ii

Given f(x) and g(x) , find f(g(5)) .

f(x)=x^4-x+15

g(x)=x^2+3x-25

Possible Answers:

50625

Undefined

225

Correct answer:

50625

Explanation:

Given f(x) and g(x), find f(g(5))

f(x)=x^4-x+15

g(x)=x^2+3x-25

This type of problem can look intimidating depending on how it is set up. What it is asking is for us to plug g(x) into f(x) everywhere we see an x, and then to plug in 5 everywhere we still have an x. It gets a little cumbersome if approached all at once:

f(g(x))=(x^2+3x-25)^4-(x^2+3x-25)+15

This looks a bit unwieldy, but this problem can be approached easily by looking at it in layers.

First, find g(5)

g(5)=(5)^2+3(5)-25=25-25+15=15

g(5)=15 .

Next, plug that 15 into f(x).

f(g(5))=f(15)=(15)^4-15+15=15^4=50625

So our answer is:

50625

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Example Question #672 : Algebra Ii

If f(x)= x^2 + 4 and g(x)= x-3 , what is f(g(x)) ?

Possible Answers:

x+1

x^2 + 1

x^2 - 2x + 3

x^2 - 6x + 13

Correct answer:

x^2 - 6x + 13

Explanation:

We start by replacing all the 's in f(x) with the entire function of g(x) :

f(g(x))= (x-3)^2 + 4

We then FOIL the first term:

f(g(x))= (x^2 - 6x + 9) +4

And we collect all the like terms (the constants in this case):

f(g(x))= x^2 - 6x + 13

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Example Question #17 : Function Notation

What is

$(f\cdot g)(x)$ ?

f(x) = -8x+8

g(x) = x^2

Possible Answers:

2x^3-4

8x^2-8

-8x^3+8x^2

8x^3 -12

4x^2-4x

Correct answer:

-8x^3+8x^2

Explanation:

To find the composition of two functions, substitute the second equation in to the first function.

$(g\cdot h)(x)=g(h(x))$

Therefore,

$(f\cdot g)(x) = (-8x+8)(x^2)$

-8x(x^2) =-8x^3

and

8(x^2) = 8x^2

Thus,

$(f\cdot g)(x)= -8x^3+8x^2$ .

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Example Question #144 : Functions And Graphs

Use the function rule to find the f(20) for the following function:

$f(x) = 30+\frac{40}{x}$

Possible Answers:

$\frac{1}{32}$

Correct answer:

Explanation:

$f(x) = 30+\frac{40}{x}$

Given f(20) , x=20 , plug the value for x into the given equation and evaluate:

$f({\color{Red} 20}) = 30+\frac{40}{{\color{Red} 20}}$

f(20) = 30+2

f(20) = 32

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Example Question #21 : Function Notation

Given g(x) =x^2+2 and h(x)=3x , what is g(h(2)) ?

Possible Answers:

$\textup{The answer is not given.}$

Correct answer:

Explanation:

The question asked is a composite function.

Evaluate h(2) first. Replace x with the value of 2 in the function h(x) .

h(2)=3(2)=6

After substitution, evaluate g(6) . Replace x with the value of 6 in the function g(x) .

g(6) =(6)^2+2 = 36+2 =38

The answer is:

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Example Question #21 : Function Notation

If f(x) = 2x+3 , what must f(-6) be?

Possible Answers:

Correct answer:

Explanation:

Replace the value of negative six into the function of x equation.

f(-6) = 2(-6)+3

Simplify this equation.

-12+3 =-9

The answer is:

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Example Question #23 : Function Notation

If f(x)=1 and $g(x)= 2x^{5}+3x^{4}+4x^{3}$ , what must f(g(50)) be?

Possible Answers:

$\textup{Cannot be solved.}$

644250000

$\frac{1}{644250000}$

Correct answer:

Explanation:

Notice that this composite function is asking for the value of of a particular number solved by evaluating g(50) . The function f(x)=1 means that no matter what the x-value inside f(x) is, the final output will always be one.

We do not even need to evaluate g(50) to determine what f(g(50)) is since we know that g(50) will yield a very large number, and that the output of the function of f(x) will be one for $x=\textup{any constant}$ .

The answer is:

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Example Question #24 : Function Notation

If f(x) = 3x-6 and g(x)= 9x-3 , what is $g(f(x))\cdot f(x)$ ?

Possible Answers:

81x^2-333x+342

81x^2+342

81x^2-342

$\textup{The answer is not given.}$

81x^2+333x-342

Correct answer:

81x^2-333x+342

Explanation:

Evaluate g(f(x)) first. Substitute the function f(x) into g(x) .

g( 3x-6)= 9( 3x-6)-3

Distribute the integer through the binomial and simplify the equation.

9( 3x-6)-3 = 27x-54-3 = 27x-57

g(f(x))=g( 3x-6)= 27x-57

Multiply this expression with f(x) .

(27x-57)(3x-6)

= (27x)(3x)+(27x)(-6)+(-57)(3x)+(-57)(-6)

81x^2-162x-171x+342

The answer is: 81x^2-333x+342

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Example Question #25 : Function Notation

If f(x) = 3x and g(x)= 3x^2 , what is 2f(x)+g(f(x)) ?

Possible Answers:

6x+ 27x^3

6x+9x^2

6x+ 27x^2

9x^2

6x+9x^3

Correct answer:

6x+ 27x^2

Explanation:

Evaluate each term separately.

2f(x)=2(3x)=6x

The term g(f(x)) means to input the function f(x) into the function g(x) .

Substitute the equation as the replacement of the x-variable.

g(f(x)) = 3(3x)^2 = 3(9x^2) = 27x^2

Add the two terms.

2f(x)+g(f(x))=6x+ 27x^2

The answer is: 6x+ 27x^2

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Example Question #26 : Function Notation

Given the function: f(x) = x^3-2(x+2) , what is f(-4) ?

Possible Answers:

Correct answer:

Explanation:

To solve this function, the term f(-4) means to replace negative four with the x-variable.

f(-4) = (-4)^3-2((-4)+2)

Use order of operations and simplify the terms on the right side.

f(-4) = -64 -2(-2)

f(-4) = -64+4 = -60

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #671 : Algebra Ii

Example Question #672 : Algebra Ii

Example Question #17 : Function Notation

Example Question #144 : Functions And Graphs

Example Question #21 : Function Notation

Example Question #21 : Function Notation

Example Question #23 : Function Notation

Example Question #24 : Function Notation

Example Question #25 : Function Notation

Example Question #26 : Function Notation

All Algebra II Resources

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