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Find the inverse function.

[tex]\[
\begin{aligned}
f(x) & = \frac{7x - 4}{2} \\
f^{-1}(x) & = \frac{2x + 4}{7}
\end{aligned}
\][/tex]



Answer :

GinnyAnswer
To find the inverse of the given function [tex]\( f(x) = \frac{7x - 4}{2} \)[/tex], we will need to follow specific steps in algebra to solve for the inverse function.

1. Set [tex]\( y = f(x) \)[/tex]:

[tex]\[ y = \frac{7x - 4}{2} \][/tex]

2. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:

Start by isolating [tex]\( x \)[/tex] in the given equation:

[tex]\[ 2y = 7x - 4 \][/tex]

Next, solve for [tex]\( 7x \)[/tex]:

[tex]\[ 7x = 2y + 4 \][/tex]

Finally, divide both sides by 7 to solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{2y + 4}{7} \][/tex]

3. Express the inverse function [tex]\( f^{-1}(x) \)[/tex]:

By replacing [tex]\( y \)[/tex] with [tex]\( x \)[/tex] in the final equation, we get:

[tex]\[ f^{-1}(x) = \frac{2x + 4}{7} \][/tex]

Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] can be written as:

[tex]\[ f^{-1}(x) = \frac{2x + 4}{7} \][/tex]

So, [tex]\( f^{-1}(x) \)[/tex] is [tex]\( \frac{2x + 4}{7} \)[/tex], where [tex]\( 2 \)[/tex], [tex]\( 4 \)[/tex], and [tex]\( 7 \)[/tex] are the coefficients of [tex]\( x \)[/tex], the constant term, and the denominator, respectively.

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