Question

Let f(x) = x2 + 6 and g(x) = x + 8x g ( x ) = x + 8 x . Find ( g o f)(­ -7)

Answer 1

(g o f)(-7) = 495

Explanation:

We have given two function .

f(x) = x²+6 and g(x) = x+8x

We have to find composition of two given function and then we have to find the value of (g o f)(-7).

The formula to find composition of two function is:

(g o f)(x) = g(f(x))

Putting the values of given function is:

(g o f)(x) = g(x²+6)

(g o f)(x) = x²+6 +8(x²+6)

Simplifying above equation , we have

(g o f)(x) = x²+6+8x²+48

Adding like terms , we have

(g o f)(x) = 9x²+54

Putting x = -7 in above equation , we have

(g o f)(-7) = 9(-7)²+54

(g o f)(-7) = 9(49) +54

(g o f)(-7) = 495 which is the answer.

Answer 2

(g o f)(-7) = 495

Explanation:

We have two functions:

`f(x) = x^2 +6\\\\g(x) = x + 8x`

To find (g o f) we must introduce the function f(x) inside the function g(x). That is, we take the function g(x) and where there is an x we place the function f(x). So:

(g o f)(x) = g(f(x))

(g o f)(x) =
`(x^2 + 6) +8(x^2 + 6)`

We simplify:

(g o f)(x) =
`x^2 + 6 + 8x^2 + 48`

(g o f)(x) =
`9x^2 + 54`

Now we have (g o f)(x). To find (g o f)(-7) we substitute x = -7 in the function:

(g o f)(-7) =
`9(-7)^2 +54`

(g o f)(-7) = 495