Question

What is the inverse of f(x)=x4+7 for x≥0 where function g is the inverse of function f?

g(x)= 4√x+7, x≥−7

g(x)= 4√x−7, x≥7

g(x)=x√4−7, x≥0

g(x)=x√4+7, x≥0

Answer 1

`\sqrt[4]{x-7}`, x
`\geq` 7

Explanation:

just took the test :D

Answer 2

`\text{Consider the function, }\\ \\ f(x)=x^4+7, \ \ \text{ for }x\geq 0\\ \\ \text{let y=f(x). so in order to find the inverse first we interchange x and y.}\\ \text{so we have}\\ \\ x=y^4+7\\ \\ \text{and now we will solve for y again and that will give the inverse function.}\\ \text{so subtract 7 both sides, we get}`

`x-7=y^4\\ \\ \text{now to get rid of exponent 4 from y, we take fourth root both sides.}\\ \text{so we get}\\ \\ \sqrt[4]{x-7}=y\\ \\ \text{hence the inverse function is }g(x)=\sqrt[4]{x-7}\\ \\ \text{we know that for a function its domain is the range of its inverse function}\\ \text{and the ragne of the function is domain of the inverse function.}\\ \\ \text{here observe that the range of f(x) is }f(x)\geq 7, \text{ domain of}`

`\text{inerse function g(x) would be }x\geq 7\\ \\ \text{hence the inverse of the function is}\\ \\ g(x)=\sqrt[4]{x-7}, \ \ \  x\geq 7`