Question

If f(x) = 5x, what is f¹(x)?

Answer 1

Answer:

C

Step-by-step explanation:

For any function x, inverse will = 1/x. so the answer is C

Answer 2

Answer:

C. $f^{-1}(x) = \frac{1}{5} x$

Step-by-step explanation:

The question is asking to find $f^{-1}(x)$ of f(x)=5x, which is the same as finding the inverse of the function.

To find the inverse of a function, we first need to replace f(x) with y.

The function will therefore be:

y = 5x

Now, we solve the equation for x.

So divide both sides by 5.

y = 5x

÷5  ÷5

_________

$\frac{y}{5} = x$

Now, we replace x with y and y with x.

$\frac{x}{5} = y$

Finally, we replace y with $f^{-1}(x)$.

$\frac{x}{5} = f^{-1}(x)$

We can re-write this though, to make it easier to read.

We can write $f^{-1}(x)$ first, and rewrite $\frac{x}{5}$ as $\frac{1}{5}x$.

$f^{-1}(x) = \frac{1}{5} x$

Therefore, the answer is C.