Question

What is the inverse of function f? F(X) = square root of x +7

Answer 1

f⁻¹=x²+7

Solution:

• In order to find the inverse of a function, we should first replace f(x) with y, then switch x and y places, like so:
• y=√x+7
• x=√y+7
• Now, solve the equation for y.
• Square both sides in order to get rid of the square root:
• x²+7=y
• y=x²+7
• And finally, replace y with f⁻¹:
• f⁻¹=x²+7
• Also, inverse functions do the opposite thing in the opposite order.
• So if we have f(x)=x+7, the inverse function is: f⁻¹=x-7

Hope it helps.

Do comment if you have any query.

Answer 2

Answer:
`f^(-1) (x)=x^(2) -7`

Explanation:

To find the inverse of a function replace f(x) with x and the original x with y

`f(x)=√(x+7) \\x=√(y+7)`

Now we can solve for y

Square both sides so we can cancel out the root

`x=√(y+7)\\x^(2) =√(y+7)^(2) \\x^(2) =y+7`

Now subtract 7 from both sides

`x^(2) =y+7\\x^(2) -7=y+7-7\\x^(2) -7=y`

Now replace y with the inverse of f(x),
`f^(-1) (x)`