Question

What is the inverse of the function f(x) = 2x – 10?

Answer 1

Answer:

$h(x)=\dfrac{x}{2}+5$

Step-by-step explanation:

You are given the function $f(x)=2x-10$. To find the inverse function $f^{-1}(x)$ do such steps:

1. Rewrite the function f(x) as

$y=2x-10$

2. Express x in terms of y:

$y+10=2x\\ \\x=\dfrac{y}{2}+5$

3. Change x into y and y into x:

$y=\dfrac{x}{2}+5$

Now, the inverse function is

$f^{-1}(x)=\dfrac{x}{2}+5$

Answer 2

Answer:

Option D.

Step-by-step explanation:

The given function is

$f(x)=2x-10$

We need to find the inverse of the function f(x).

Step 1 : Substitute f(x)=y.

$y=2x-10$

Step 2: Interchange x and y.

$x=2y-10$

Step 3: Isolate variable y.

$x+10=2y$

$\frac{x+10}{2}=y$

$\frac{x}{2}+\frac{10}{2}=y$

$\frac{x}{2}+5=y$

$y=\frac{x}{2}+5$

Step 4: Substitute y=h(x).

$h(x)=\frac{1}{2}x+5$

The inverse of the function f(x) is $h(x)=\frac{1}{2}x+5$.

Therefore, the correct option is D.