Question

Let $y=f(x)=m x+b$ $m \neq 0$ (a) Writing to Learn Give a convincing argument that $f$ is a one-to-one function. (b) Find a formula for the inverse of $f .$ How are the slopes of $f$ and $f^{-1}$ related? (c) If the graphs of two functions are parallel lines with a nonzero slope, what can you say about the graphs of the inverses of the functions? (d) If the graphs of two functions are perpendicular lines with a nonzero slope, what can you say about the graphs of the inverses of the functions?

          Let $y=f(x)=m x+b$ $m \neq 0$
(a) Writing to Learn Give a convincing argument that $f$ is a one-to-one function.
(b) Find a formula for the inverse of $f .$ How are the slopes of $f$ and $f^{-1}$ related?
(c) If the graphs of two functions are parallel lines with a nonzero slope, what can you say about the graphs of the inverses of the functions?
(d) If the graphs of two functions are perpendicular lines with a nonzero slope, what can you say about the graphs of the inverses of the functions?

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Added by Rafael J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Oscar Bender-Stone

06/30/2022

Step 1

Given $f(x) = mx + b$, we have $mx_1 + b = mx_2 + b$. Subtracting $b$ from both sides gives $mx_1 = mx_2$. Dividing by $m$ (assuming $m \neq 0$) gives $x_1 = x_2$. Therefore, $f$ is one-to-one. ** Show more…

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Let $y=f(x)=m x+b$ $m \neq 0$ (a) Writing to Learn Give a convincing argument that $f$ is a one-to-one function. (b) Find a formula for the inverse of $f .$ How are the slopes of $f$ and $f^{-1}$ related? (c) If the graphs of two functions are parallel lines with a nonzero slope, what can you say about the graphs of the inverses of the functions? (d) If the graphs of two functions are perpendicular lines with a nonzero slope, what can you say about the graphs of the inverses of the functions?

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