MATH SOLVE

2 months ago

Q:
# Given the function f(x) =3(x+2)-4, solve for the inverse function when x=2

Accepted Solution

A:

The inverse function is f(x) = [tex] \frac{x + 4}{3} - 2 [/tex], which makes the inverse at x = 2 equal to 0.

All inverse functions can be found by switching the x and f(x) values. Once that is done, solve for the new f(x) value. The result will be the inverse of the original function. The step-by-step process is below.

f(x) = 3(x + 2) - 4 ----> Switch the x and f(x) x = 3(f(x) + 2) - 4 ----> Add 4 to both sidesx + 4 = 3(f(x) + 2) ----> Divide both sides by 3[tex] \frac{x + 4}{3} [/tex] = f(x) + 2 ----> Subtract 2 from both sides. f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]

The end is your inverse function. So then we can evaluate when x = 2.

f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]f(2) = [tex] \frac{2 + 4}{3} - 2 [/tex]f(2) = [tex] \frac{6}{3} - 2 [/tex]f(2) = [tex] 2 - 2 [/tex]f(2) = 0

All inverse functions can be found by switching the x and f(x) values. Once that is done, solve for the new f(x) value. The result will be the inverse of the original function. The step-by-step process is below.

f(x) = 3(x + 2) - 4 ----> Switch the x and f(x) x = 3(f(x) + 2) - 4 ----> Add 4 to both sidesx + 4 = 3(f(x) + 2) ----> Divide both sides by 3[tex] \frac{x + 4}{3} [/tex] = f(x) + 2 ----> Subtract 2 from both sides. f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]

The end is your inverse function. So then we can evaluate when x = 2.

f(x) = [tex] \frac{x + 4}{3} - 2 [/tex]f(2) = [tex] \frac{2 + 4}{3} - 2 [/tex]f(2) = [tex] \frac{6}{3} - 2 [/tex]f(2) = [tex] 2 - 2 [/tex]f(2) = 0