Given the function f(x) = log5(x + 1), find the value of f−1(2). f−1(2) = 3 f−1(2) = 11 f−1(2) = 18 f−1(2) = 24

Answer: 24

Explanation

1) The given function is understood to be f(x) = logaritm base 5 of (x + 1)

That is:

[tex]f(x)=log_5(x+1)[/tex]

2) You want  f−1(2), which is the inverse function at x = 2

And the options are:

 f−1(2) = 3
 f−1(2) = 11
 f−1(2) = 18
 f−1(2) = 24

The answser is the fourth option 24.

This is how you find it.

1) The inverse fucntion of

[tex]f(x) = y = log_5(x+1)[/tex]

is

[tex]5^y=x+1[/tex]

Swap x and y:

5ˣ = y + 1

From which, it follows:

y = 5ˣ - 1

Now just replace x = 2

=> y = 5² - 1 = 25 - 1 = 24

Which is the answer (the fourth option).