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

The inverse of the given function is $h(x) = \frac{x}{2} - \frac{1}{2}$.

Step-by-step explanation:

Given, f(x) = 2x + 1

Let f(x) = y,   y = 2x + 1

Swap variables x and y,

x = 2y + 1

Now solve for y,

=> 2y = x - 1

=> y = $\frac{x}{2} - \frac{1}{2}$

=> $f^{-1}{(x)} = \frac{x}{2} - \frac{1}{2}$

=> h(x) = $\frac{x}{2} - \frac{1}{2}$

Hence, the inverse of the given function is $h(x) = \frac{x}{2} - \frac{1}{2}$.