Question

Hello :)

f : R ⇒ R

f( x ) = 5 - x

if, f⁻¹ Which of the following?

A) 5 + x
B) 5 - x
C) -5 - x
D) 5x
E) -x/5

answer -- B

Answer 1

B

Explanation:

• Rule => f(x)=a , f⁻¹(a)=x

So ; f⁻¹(5-x)=x

plug in ''-x+5'' for x

f⁻¹(5-x)=x

f⁻¹(5-(-x + 5))=-x + 5

f⁻¹(5 +x -5 )= -x + 5

f⁻¹(x)= 5 - x

Hope this helps ^-^

Answer 2

B) 5 - x

Explanation:

`\text{We have}\ f(x)=5-x\to y=5-x\\\\\text{exchange x to y:}\ x=5-y\\\\\text{Solve for y:}\\\\5-y=x\qquad\text{subtract 5 from both sides}\\\\-y=x-5\qquad\text{change the signs}\\\\y=-x+5\\\\y=5+(-x)\\\\y=5-x\to f^(-1)(x)=5-x`