Answer:
[tex]h(x)=\dfrac{x}{2}+5[/tex]
Step-by-step explanation:
You are given the function [tex]f(x)=2x-10[/tex]. To find the inverse function [tex]f^{-1}(x)[/tex] do such steps:
1. Rewrite the function f(x) as
[tex]y=2x-10[/tex]
2. Express x in terms of y:
[tex]y+10=2x\\ \\x=\dfrac{y}{2}+5[/tex]
3. Change x into y and y into x:
[tex]y=\dfrac{x}{2}+5[/tex]
Now, the inverse function is
[tex]f^{-1}(x)=\dfrac{x}{2}+5[/tex]
Answer:
Option D.
Step-by-step explanation:
The given function is
[tex]f(x)=2x-10[/tex]
We need to find the inverse of the function f(x).
Step 1 : Substitute f(x)=y.
[tex]y=2x-10[/tex]
Step 2: Interchange x and y.
[tex]x=2y-10[/tex]
Step 3: Isolate variable y.
[tex]x+10=2y[/tex]
[tex]\frac{x+10}{2}=y[/tex]
[tex]\frac{x}{2}+\frac{10}{2}=y[/tex]
[tex]\frac{x}{2}+5=y[/tex]
[tex]y=\frac{x}{2}+5[/tex]
Step 4: Substitute y=h(x).
[tex]h(x)=\frac{1}{2}x+5[/tex]
The inverse of the function f(x) is [tex]h(x)=\frac{1}{2}x+5[/tex].
Therefore, the correct option is D.
