Question

If f(x) = 5x, what is f–1(x)?

f–1(x) = –5x

f-1(x) = -1/5x

f-1(x) = 1/5x

f–1(x) = 5x

Answer 1

$f(x)=5x\to y=5x$

We exchange x with y and solve the equation for y

$5y=x\ \ \ \ |:5\\\\y=\dfrac{x}{5}\\\\y=\dfrac{1}{5}x$

Answer: $f^{-1}(x)=\dfrac{1}{5}x$

Answer 2

The value of f^-1 (x)

What is inverse of function?

Inverse function is represented by f-1 with regards to the original function f and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

Steps To Find An Inverse Function

The following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps.

• For the given function f(x) = ax + b, replace f(x) = y, to obtain y = ax + b.
• Interchange the x with y and the y with x in the function y = ax + b to obtain x = ay + b.
• Here solve the expression x = ay + b for y. And we obtain y = (x - b/a
• Finally replace y = f-1(x), and we have f-1(x) = (x - b)/a.

Given:

f(x) = 5x

let f(x)= y

So, y= 5x

x= y/5

Hence, f^-1(x)= y/5

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