Question
The functions f and g are as follows :
f(x) = 1 (x+1)² g(x) = 1/x
A) Find g⁻¹(x)
B) gf(x)
C) Solve for gf(x)=16
x = __ or x = __
f(x) = 1 (x+1)² g(x) = 1/x
A) Find g⁻¹(x)
B) gf(x)
C) Solve for gf(x)=16
x = __ or x = __
Answers
oobleck
(A) 1/x is its own inverse, since 1/(1/x) = x
(B) gf(x) = g(x) * f(x)
I cannot interpret the space in f(x), but if f(x) = 1/(x+1)^2 then
gf(x) = 1/(x(x+1)^2)
Now, if you meant (g◦f)(x) then that is g(f(x) = 1/(f(x)^2) = (x+1)^4
(C) Pick your gf answer and just set it to 16 and solve for x. I suspect you wanted (g◦f), since (±2)^4 = 16
(B) gf(x) = g(x) * f(x)
I cannot interpret the space in f(x), but if f(x) = 1/(x+1)^2 then
gf(x) = 1/(x(x+1)^2)
Now, if you meant (g◦f)(x) then that is g(f(x) = 1/(f(x)^2) = (x+1)^4
(C) Pick your gf answer and just set it to 16 and solve for x. I suspect you wanted (g◦f), since (±2)^4 = 16