Question

nc math 3 - binns thompson functions skills drill
functions skills drill
due sep 4 by 11:59pm points 30
submitting an external tool
available sep 4 at 11am - oct 24 at 11:59pm
find the inverse function of the function $f(x)=\frac{1}{4}x + 5$.
answer
$f^{-1}(x)=-4x - 5$
$f^{-1}(x)=4x - 20$
$f^{-1}(x)=-4x - 20$
$f^{-1}(x)=4x - 5$

Explanation:

Step1: Set \(y = f(x)\)

Let \(y=\frac{1}{4}x + 5\).

Step2: Solve for \(x\) in terms of \(y\)

First, subtract 5 from both sides: \(y - 5=\frac{1}{4}x\). Then multiply both sides by 4 to get \(x = 4(y - 5)=4y-20\).

Step3: Replace \(x\) with \(f^{-1}(x)\) and \(y\) with \(x\)

We have \(f^{-1}(x)=4x - 20\).

Answer:

B. \(f^{-1}(x)=4x - 20\)