What is the inverse of the function f(x)=x/5-2

Question

asked Aug 24, 2023 38.3k views

1 Answer

Jayprakash Dubey · Answer 1 · 2023-08-28T11:38:19+0000

Answer:

$\huge\boxed{\sf f^(-1)(x)=5x+10}$

Explanation:

$\displaystyle f(x)=(x)/(5) -2$

Put f(x) = y

$\displaystyle y=(x)/(5) -2$

Swap x and y

$\displaystyle x = (y)/(5) -2$

Now, solve for y

$\displaystyle x = (y)/(5) -2$

Add 2 to both sides

$\displaystyle x + 2 =(y)/(5)$

Multiply 5 to both sides

5(x+2)=y

Distribute

5x + 10 =y

Put y = f⁻¹(x)

$\boxed{f^(-1)(x)=5x+10}$

$\rule[225]{225}{2}$