Question

Which function below is the inverse of f(x) = X2 - 25?

Answer 1

⇒Note for inverses we swap the positions between x and y.

⇒
`x=y^(2) -25\\`

But in this case we know that we write the equation such that the variable for the input is the subject of the equation

`y^(2)= x+25\\y=√(x+25)`

Note y in this case was representing f(x)

⇒therefore our final equation now is

`f(x)=√(x+25)`

GOODLUCK!!!

Answer 2

Answer:
`f^(-1)(x)= √(x+25)` and
`f^(-1)(x)= - √(x+25)`

Explanation:

To find the inverse, we will set f(x) equal to y, swap the x and y values, and then solve for y.

Given:

f(x) = x² - 25

Equal to y:

y = x² - 25

Swamp x and y values:

x = y² - 25

Add 25 to both sides of the equation:

y² = x + 25

Square root both sides of the equation:

`y= √(x+25)` and
`y= -√(x+25)`

Interval notation:

`f^(-1)(x)= √(x+25),\text{and}\;f^(-1)(x)= -√(x+25)`