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f(x)=x+4 g(x)=6-x^(2) What is the ...

`f(x)=x+4`
`g(x)=6-x^(2)`
What is the maximum value of `g(f(x))` ?

A

`-6`

B

`-4`

C

2

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`g(f(x))` is a compound function. Since `f(x)=x+4, g(f(x))=6-(x+4)^(2)`
Once you have figured out the compound function, you answer this question with the help of a graphing calculator, which will indicate the highest point of the graph. Alternatively, you can find the maximum of the function by first finding the minimym value of the squared binomial. `(x+4)^(2)` has a minimum value of zero, since a square never has a value less than 0. Six minus 0 equal 6, and that is the maximum value of the function `g(f(x))`, which occurs when `x=-4`. For any value of x other than `-4, (x+4)^(2)` will be greater than 0, so the function will have a value less than 6.
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