Question

Given the functions f(g)=(x)/(4)+ˣ²,x(y)=y-1 and g(x)=x+6, what is the value of fgx(y) if y=5 ?

Answer 1

To find the value of fgx(y) if y = 5, substitute the value of y into the given functions and perform the operations step by step. The value of fgx(y) when y = 5 is 102.5.

Step-by-step explanation:

To find the value of fgx(y) if y = 5, we need to substitute the value of y into the given functions and perform the operations step by step.

Given f(g) = (x/4) + x^2, g(x) = x + 6, and x(y) = y - 1:

1. First, we substitute y = 5 into x(y) to find the value of x:
2. x(y) = y - 1 = 5 - 1 = 4
3. Next, we substitute x = 4 into g(x) to find the value of g:
4. g(x) = x + 6 = 4 + 6 = 10
5. Finally, we substitute g = 10 into f(g) to find the value of fgx(y):
6. f(g) = (x/4) + x^2 = (10/4) + 10^2 = 2.5 + 100 = 102.5

Therefore, the value of fgx(y) when y = 5 is 102.5.