Question

deltamath
inverse of functions 3
5.3 inverses of functions
due december 11 at 11:59 pm
grade: 55%
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question
find $f^{-1}(x)$ if $f(x) = -4x + 22$.
answer attempt 1 out of 99
additional solution no solution
$f^{-1}(x) = $
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Explanation:

Step1: Swap x and y

Let \( y = f(x)= -4x + 22 \). Swap \( x \) and \( y \), we get \( x = -4y + 22 \).

Step2: Solve for y

First, subtract 22 from both sides: \( x - 22 = -4y \). Then, divide both sides by -4: \( y=\frac{22 - x}{4}=-\frac{x}{4}+\frac{11}{2} \). So \( f^{-1}(x)=-\frac{x}{4}+\frac{11}{2} \) (or can be written as \( \frac{-x + 22}{4} \)).

Answer:

\( f^{-1}(x)=-\frac{1}{4}x+\frac{11}{2} \) (or equivalent forms like \( \frac{22 - x}{4} \))