Question

Given f(x) = 1/2x - 5, find f^-1(x)

a. f^-1 (x) = -2x+10
b. f^-1(x) = 2x+5
c. f^-1(x) = 2x-10
d. f^-1(x) = 2x+10

Answer 1

f^-1(x) = 2x + 10 → d

let y = $\frac{1}{2}$ x - 5

rearrange making x the subject

$\frac{1}{2}$ x - 5 = y

add 5 to both sides

$\frac{1}{2}$ x = y + 5

multiply both sides by 2

x = 2y + 10 ⇒ f^-1(x) = 2x + 10

s

Answer 2

The inverse function for the given function f(x) = 1/2x - 5 is $f^-^1(x) = 2x+10$.

This is obtained by interchanging the dependent and independent variables.

What is an inverse function?

In an inverse function, the independent variable interchanges with the dependent variable. I.e., if a function f takes x to y then the inverse function f^-1 takes y to x.

Calculating the inverse function for the given function:

Given function is f(x) = 1/2x - 5

Step 1: Considering f(x) = y

So,

y = 1/2x - 5

Step 2: Solving for x

adding 5 on both sides

y + 5 = 1/2x

multiplying 2 on both sides

2(y + 5) = x

⇒ x = 2y +10

Step 3: Interchanging x to y

⇒ y = 2x + 10

Since f(y) = x then $f^-^1(x) =y$

So,

$f^-^1(x) =2x + 10$

Therefore, the inverse function is $f^-^1(x) =2x + 10$. So, option d is correct.

Learn more about inverse functions here:

https://brainly.com/question/3831584

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