Answered

Get expert advice and community support for all your questions on IDNLearn.com. Explore a wide array of topics and find reliable answers from our experienced community members.

Find the inverse of each of the given functions.

[tex]\[
\begin{array}{l}
f(x) = 4x - 12 \\
f^{-1}(x) = \square x + \square
\end{array}
\][/tex]

[tex]\[ h(x) = \frac{2x - 4}{3} \][/tex]

[tex]\[ h^{-1}(x) = \frac{3x - 12}{2} \][/tex]

Sagot :

GinnyAnsweridn
Let's find the inverse of the given function [tex]\( f(x) = 4x - 12 \)[/tex].

### Step-by-Step Solution

1. Write the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 4x - 12 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. This represents the inverse relationship:
[tex]\[ x = 4y - 12 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x + 12 = 4y \][/tex]
[tex]\[ y = \frac{x + 12}{4} \][/tex]

4. Rewrite the expression to identify the coefficients:
[tex]\[ y = \frac{1}{4}x + 3 \][/tex]

So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{1}{4}x + 3 \][/tex]

Thus, the coefficients for [tex]\( f^{-1}(x) \)[/tex] are:
[tex]\[ \begin{array}{l} f^{-1}(x) = 0.25x + 3.0 \end{array} \][/tex]

### Summary
The inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 4x - 12 \)[/tex] is:
\[
f^{-1}(x) = 0.25x + 3.0 \
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.