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Pearson Algebra 2 Common Core, 2011 View details

2. Properties of Exponential Functions

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Exercise 46 Page 450

When you are given a composite function written as (g ∘ f)(x), think of this as g(f(x)). Use the function rule of f(x) as the input for g(x) to find g(f(x)).

(g ∘ f)(x)=1/x^2

Practice makes perfect

When we are given a composite function written as (g ∘ f)(x), we can think of this as g(f(x)). (g ∘ f)(x) ⇔ g(f(x))To find g(f(x)), we will use f(x) as the input for g(x). g(x)=1/x+4 ⇒ g( f(x))=1/f(x)+4 Let's now find an expression for g(f(x)).

g(f(x))=1/f(x)+4

Substitute

f(x)= x^2-4

g( x^2-4)=1/x^2-4+4

SubTerm

Subtract term

g(x^2-4)=1/x^2

As a result, g(f(x))= 1x^2.