Given f(x) = 1/x+1 and g(x)--2x algebraically find the following

Question

asked Jul 16, 2023 110k views

1 Answer

Ragfield · Answer 1 · 2023-07-21T04:05:51+0000

Answer:

f^(-1)(x) = (1)/(x) - 1

g^(-1)(x) = (x^2)/(2)

Explanation:

For f(x):

Let y = f(x) =
(1)/(x+1)

Replace x with y:

x=(1)/(y+1)

Solve for y:

y+1 = (1)/(x)

y = (1)/(x) - 1 = f^(-1)(x)

For g(x)

Let y = g(x) =
√(2x)

Replace x with y

x=√(2y)

Solve for y

$x^2 = 2y\\y = (x^2)/(2)$ =
g^(-1)(x)