Question

What is the inverse of the function f(x) = 2x + 1?

h(x) = one-halfx – one-half
h(x) = one-halfx + one-half
h(x) = one-halfx – 2
h(x) = one-halfx + 2

Answer 1

Explanation:

for the inverse function we simply try to turn y and x around, and find the equation that calculates x out of y instead of y out of x.

remember,

f(x) = y

so, we have

y = 2x + 1

y - 1 = 2x

x = y/2 - 1/2

now we just rename x to y and y to x to make this a "normal" function :

y = h(x) = x/2 - 1/2

so, the first answer option is correct.

Answer 2

(a) h(x) = 1/2x -1/2

Explanation:

The inverse of the function y = f(x) is found by solving x = f(y).

__

setup

x = f(y)

x = 2y +1 . . . . . . use the definition of f(x)

solution

x -1 = 2y . . . . . subtract 1

(x -1)/2 = y . . . . divide by 2

y = 1/2x -1/2 . . . . eliminate parentheses

h(x) = 1/2x -1/2 . . . write in functional form

The inverse of f(x) = 2x+1 is ...

h(x) = 1/2x -1/2