Question

If f(x)=x^2+7, what is the equation for f^-1(x)???

Answer 1

So...
f(x)=x^2+7
Consider the output as being y.
y=x^2+7
Thinking of this as a step-by-step procedure (namely , take a number x , square it and then add 7 ) , to reverse this , we have to solve for x the equation y=x^2+7 .

y=x^2+7
x^2=y-7


`x=\pm√(y-7)`


`\implies f^(-1)(x)=\pm√(y-7)`

I think the answer is correct now...

Answer 2

Given: f(x) = x² + 7

Let y = x² + 7
x = y² + 7 (since the inverse is reflected about the y = x line, the coordinates are interchangeable)

y² = x - 7
y = √(x - 7)

Thus, the inverse function f^(-1)x = √(x - 7)