Answer to Question #247918 in Algebra for Raze

Question

Illustrate the graph of the given one-to-one function and its inverse.
Activity 13.2
1. f(x) = 3x - 4
2. f(x) = 5x + 3
3. f(x) = 7-5
4. f(x)
x-2
3
5. f(x)
x + 3
2​

Answer 1

1 $f(x)=3x-4 \implies f^{-1}(x)=\frac{x+4}{3}$

Below is the graph of $f(x)$(color green) and $f^{-1}(x)$ (color red)

2 $f(x)=5x+3 \implies f^{-1}(x)=\frac{x-3}{5}$

Below is the graph of $f(x)$(color green) and $f^{-1}(x)$ (color red)

3 $f(x)=7x-5 \implies f^{-1}(x)=\frac{x+5}{7}$

Below is the graph of $f(x)$(color green) and $f^{-1}(x)$ (color red)

4 $f(x)=\frac{x-2}{3} \implies f^{-1}(x)=3x+2$

Below is the graph of $f(x)$(color green) and $f^{-1}(x)$ (color red)

5 $f(x)=\frac{x+3}{2} \implies f^{-1}(x)=2x-3$

Below is the graph of $f(x)$(color green) and $f^{-1}(x)$ (color red)