College

28. Given the function [tex]f(x) = \log(x + 1)[/tex], find the value of [tex]f(2)[/tex].

A. [tex]f(2) = -3[/tex]
B. [tex]f(2) = 11[/tex]
C. [tex]f(2) = 18[/tex]
D. [tex]f(2) = 24[/tex]

Answer :

Given that

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

To solve the question, we will have to first find the inverse of the function

[tex]f(x)=\text{ y = }log_5(x+1)[/tex][tex]5^y\text{ =x + 1}[/tex]

Make x the subject of the formula

[tex]x=5^y\text{ - 1}[/tex]

The inverse of the function is:

[tex]f^{-1}(x)=5^x\text{ - 1}[/tex]

Substituting x = 2

[tex]\begin{gathered} f^{-1}(2)=5^2\text{ - 1} \\ f^{-1}(2)=25\text{ - 1} \\ \\ f^{-1}(2)=24 \end{gathered}[/tex]

Answer = 24

Option D is correct

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