let f(x)= 4+(3x+7)^3 , find f^-1(x) = , find(f(x))^-1

Answer 1

To find the inverse of a function f(x), you write the equation

y = f(x)

and then represent x in terms of y.

y = 4 + (3x+7)³

y-4 = (3x+7)³

(y-4)^1/3 = 3x+7

(y-4)^1/3 - 7 = 3x

((y-4)^1/3 - 7)/3 = x

Therefore we can write

f(y) = ((y-4)^1/3 - 7)/3

Or use the variable name x

f(x) = ((x-4)^1/3 - 7)/3

In contrast, (f(x))^-1 is simply

(f(x))^-1 = 1/f(x) = 1/(4 + (3x+7)³)