Question

Consider the function f(x) = √5x + 15 for the domain [-3, ∞).Find f-¹(x), where f-1 is the inverse of f.Also state the domain of f¹ in interval notation.

Answer 1

Answer: We have to find the inverse function of the following:

`f(x)=√(5x+15)\rightarrow[-3,\infty)\Rightarrow(1)`

The Inverse of the (1) is as follows:

`\begin{gathered} f(x)=y=√(5x+15) \\ \\ \text{ Switch: }x\text{ and }y\text{ and solve for }y(x)\text{ } \\ \\ \\ y=√(5x+15)\rightarrow x=√(5y+15) \\ \\ \\ x^2=5y+15 \\ \\ \\ x^2-15=5y \\ \\ \\ y=(x^2)/(5)-(15)/(5) \\ \\ \\ \\ y=f^(-1)(x)=(x^2)/(5)-3 \\ \\ \\ f^(-1)(x)=(x^(2))/(5)-3 \end{gathered}`

The domain of the inverse function is:

`x\in(-\infty,+\infty)`