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Chapter 5: Q 47. (page 257)

In Problems 45鈥�52, show that (f鈭�g)(x)=(g鈭�f)(x)=x

f(x)=x3;g(x)=x3

Short Answer

Expert verified

(f鈭�g)(x)=x(g鈭�f)(x)=x

Therefore,(f鈭�g)(x)=(g鈭�f)(x)=x.

Step by step solution

01

Step 1. Given information.

The given composite function is:

f(x)=x3g(x)=x3

When we are given two functions f and g, the composite function which is denoted by f鈭�gis defined by (f鈭�g)(x)=f(g(x)).

02

Step 2. Find (f∘g)(x).

(f鈭�g)(x)=f(g(x))

Now substitute g(x)=x3in the function f(g(x)),

Then the function will become f(x3),

role="math" localid="1646299268382" f(x3)=((x3))3=x

Therefore,(f鈭�g)(x)=x.

03

Step 3. Find (g∘f)(x).

(g鈭�f)(x)=g(f(x))

Substitutef(x)=x3ing(f(x)),

(g鈭�f)(x)=g(f(x))=g(x3)=x33=x

(g鈭�f)(x)=x

It is shown that(f鈭�g)(x)=(g鈭�f)(x)=x.

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Most popular questions from this chapter

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x+1x

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=-2xx-1

Solve the equation2-x=16

and verify your results using a graphing utility

In Problems 33-40, the graph of an exponential function is given. Match each graph to one of the following functions.
See all solutions

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