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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

6. Natural Logarithms

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Exercise 68 Page 483

When given a composite function written as (g ∘ f)(x), think of it as g(f(x)).

958

Practice makes perfect

When we are given a composite function written as (g ∘ f)(x), we can think of it as g(f(x)). (g ∘ f)(x) ⇔ g(f(x))To find the value of (g ∘ f)(6), we will first evaluate f(6).

f(x)=5-x^2

x= 6

f( 6)=5- 6^2

Calculate power

f(6)=5-36

Subtract term

f(6)=- 31

Next, we will use f(6)=- 31 as the input for g(x).

g(x)=x^2-3

x= - 31

g( - 31)=( - 31)^2-3

NegBaseToPosBase

(- a)^2=a^2

g(- 31)=31^2-3

Calculate power

g(- 31)=961 - 3

Subtract term

g(- 31)=958

Therefore, (g ∘ f)(6)=958.

Subchapter links

Lesson Check p.480

Practice and Problem-Solving Exercises p.481-483

Standardized Test Prep p.483

Mixed Review p.483