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Chapter 5: Q. 61 (page 257)

If f(x)=2x2+5and g(x)=3x+a, find a so that the graph of f鈭�g crosses the y-axis at 23.

Short Answer

Expert verified

The value ofais卤3.

Step by step solution

01

Step 1. Given Information

Given thatf(x)=2x2+5and g(x)=3x+a,value off鈭�gx=23atx=0.

02

Step 2. Solution

We know that f鈭�g(x)=f(g(x)).

Here, f(x)=2x2+5and g(x)=3x+a.

So, f鈭�g(x)=f(g(x))f鈭�g(x)=2(g(x))2+5 f鈭�g(x)=2(3x+a)2+5 f鈭�g(x)=2{9x2+6xa+a2}+5f鈭�g(x)=18x2+12xa+2a2+5

So, at x=0, f鈭�g(x)=23.

Now,

atx=0,f鈭�g0=18(0)2+12(0)(a)+2a2+523=0+0+2a2+52a2=18a2=9a=卤3.

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Most popular questions from this chapter

True or False. The domain of the composite functionf鈭�gxis the same as the domain ofg(x).

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=2-e-x/2

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

localid="1646160286433" fx=5-e-x

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

f(x)=23+x

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.
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