Answer:
(g o f)(-7) = 495
Step-by-step explanation:
We have two functions:
[tex]f(x) = x^2 +6\\\\g(x) = x + 8x[/tex]
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) = [tex](x^2 + 6) +8(x^2 + 6)[/tex]
We simplify:
(g o f)(x) = [tex]x^2 + 6 + 8x^2 + 48[/tex]
(g o f)(x) = [tex]9x^2 + 54[/tex]
Now we have (g o f)(x). To find (g o f)(-7) we substitute x = -7 in the function:
(g o f)(-7) = [tex]9(-7)^2 +54[/tex]
(g o f)(-7) = 495
Answer:
(g o f)(-7) = 495
Step-by-step 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.
