Question

Given the function f(x) = 4(x+3) − 5, solve for the inverse function when x = 3. (1 point)

Answer 1

the function f(x) = 4(x+3) − 5

Lets find the inverse function f^-1(x)

step 1: Replace f(x) with y

y = 4(x+3) − 5

step 2: Replace x  with y and y with x

x = 4(y+3) - 5

step 3: Solve for y

x = 4(y+3) - 5

x = 4y +12 -5

x= 4y + 7 (subtract 7 on both sides)

x - 7 = 4y (divide by 4 on both sides)

$\frac{x-7}{4}=y$

$f^{-1}(x)=\frac{x-7}{4}$

Given : x = 3

We plug in 3 for x in the inverse function

$f^{-1}(x)=\frac{3-7}{4}$ = -1

the inverse function when x = 3  is -1

Answer 2

the inverse function is x = 3  is -1