Question

hsm3
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5.1.2 graphing inverse practice
find the inverse of each function. then graph the function and its inverse.

1. ( f(x) = 4 + \frac{7}{5}x )
2. ( f(x) = -x - 4 )

name anncbelln
date

1. ( f(x) = -\frac{2}{}x + \frac{4}{} ) (note: some parts of the 4th functions expression seem incomplete in the ocr, but the main visible functions are as above)

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 4 + \frac{7}{5}x$

Step2: Swap $x$ and $y$

$x = 4 + \frac{7}{5}y$

Step3: Isolate the term with $y$

$x - 4 = \frac{7}{5}y$

Step4: Solve for $y$

$y = \frac{5}{7}(x - 4) = \frac{5}{7}x - \frac{20}{7}$
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Step1: Replace $f(x)$ with $y$

$y = -x - 4$

Step2: Swap $x$ and $y$

$x = -y - 4$

Step3: Isolate the term with $y$

$x + 4 = -y$

Step4: Solve for $y$

$y = -x - 4$
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Step1: Replace $f(x)$ with $y$

$y = -\frac{2}{5}x + \frac{4}{5}$

Step2: Swap $x$ and $y$

$x = -\frac{2}{5}y + \frac{4}{5}$

Step3: Isolate the term with $y$

$x - \frac{4}{5} = -\frac{2}{5}y$

Step4: Solve for $y$

$y = -\frac{5}{2}x + 2$

Answer:

1. Inverse function: $f^{-1}(x) = \frac{5}{7}x - \frac{20}{7}$

• To graph $f(x)=4+\frac{7}{5}x$: use intercepts $(0,4)$ and $(-\frac{20}{7},0)$; to graph its inverse, plot points swapped from $f(x)$ (e.g., $(4,0)$ and $(0,-\frac{20}{7})$) and draw the line, symmetric over $y=x$.

1. Inverse function: $f^{-1}(x) = -x - 4$

• This function is its own inverse. Graph the line with intercepts $(0,-4)$ and $(-4,0)$; it is symmetric over $y=x$.

1. Inverse function: $f^{-1}(x) = -\frac{5}{2}x + 2$

• To graph $f(x)=-\frac{2}{5}x+\frac{4}{5}$: use intercepts $(0,\frac{4}{5})$ and $(2,0)$; to graph its inverse, plot swapped points (e.g., $(\frac{4}{5},0)$ and $(0,2)$) and draw the line, symmetric over $y=x$.