Question

F(x)=3√x + 7. Find the inverse of f(x).

Answer 1

f(x)=(x^2-14x+49)/9


step 1- switch x and y
step 2- isolate y, and get to (x-7)/3=sqrty
step 3- square each side to get rid of the square root and isolate y
step 4- f(x)=(x^2-14x+49)/9

Answer 2

`f^(-1)(x)=\left((x-7)/(3)\right)^2`

Explanation:

Given function:

`f(x)=3√(x)+7`

To find the inverse of the function

Swap f(x) for y:

`\implies y=3 √(x)+7`

Subtract 7 from both sides:

`\implies y-7=3 √(x)+7-7`

`\implies y-7=3√(x)`

Divide both sides by 3:

`\implies (3√(x))/(3)=(y-7)/(3)`

`\implies √(x)=(y-7)/(3)`

Square both sides:

`\implies \left(√(x)\right)^2=\left((y-7)/(3)\right)^2`

`\implies x=\left((y-7)/(3)\right)^2`

Swap the x for
`f^(-1)(x)` and y for x:

`\implies f^(-1)(x)=\left((x-7)/(3)\right)^2`