Question

Find (g*f)(3)
f(x)= |x+2|
g(x)= -x2

Answer 1

(gof)(3) = -25

Explanation:

We have given two functions.

f(x)= |x+2|

g(x)= -x²

We have to find (gof)(3).

(gof)(x) = ? and (gof)(3) = ?

(gof)(x) = g(f(x))

(gof)(x) = g( |x+2|)

(gof)(x) = -( |x+2|)²

Since, we know that

( |x|)² = x²

hence, (gof)(x) = -(x+2)²

Putting x = 3 in above equation, we have

(gof)(3) =-(3+2)²

(gof)(3) = -(5)²

(gof)(3) = -25 which is the answer

Answer 2

Option a.
`(gof)(3) = -25`

Explanation:

They ask us to find

(gof)(3)

To solve this problem we must introduce the function f(x) within the function g(x)

That is, we must do g(f(x)).

So, we have:

`f(x) = |x + 2|\\\\g(x) = -x^2`

Then:

`g(f(x)) = -(|x + 2|) ^ 2`

This is:

`g(f(x)) = -(x + 2) ^ 2`

Now we must do x = 3

`g(f(3)) = -(3 + 2) ^ 2`

`(gof)(3) = -25.`

The answer is:
`(gof)(3) = -25.`