Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

`f^(-1)(x) = 4x^(2)-3, for  x\leq -3`

Explanation:

The given equation is ,

`f(x) = y = ((-1)/(2))(√(x+3) )`

For finding the inverse, we write the equation of x as function of y, and then rewrite replacing x with y and y with x.

Thus, the equation formed is inverse of the given equation.

`f(x) = y = ((-1)/(2))(√(x+3) )`

`(-2)y = (√(x+3) )`, squaring both the sides.

`4y^(2)=x+3`

`x = 4y^(2)-3`, now replace x with y and y with x.

Thus,
`y = 4x^(2)-3`, where x
`\leq` -3.