Domain and Range pre- calc question

Question

Determine the inverse of the one-to-one function 𝑓(𝑥) = 3−4𝑥 7+8𝑥

State the domain and range of the inverse

Answer 1

f(x) = 3 -4x

domain and range are all real numbers

It's a straight line with slope = -4 and y intercept = 3, x intercept = 3/4

y = 3-4x

switch the x and y

x = 3-4y

solve for y

4y=3-x

y = (3-x)/4

f^-1(x)= 3/4 -x/4

domain and range are all real numbers

It's a straight line with slope =-1/4, y intercept = 3/4, x intercept = 3

The 1st line and its inverse are symmetric about the line y=x

f(x) =7+8x

domain and range are all real numbers

It's a straight line with slope = 8, y intercept = 7, x intercept =-8/7

y= 7+8x

switch x and y

x=7+8y

solve for y

8y =x-7

y = x/8 - 7/8

domain and range are all real numbers

It's a straight line with slope = 1/8, y intercept =-7/8, x intercept = 7

y=7+8x and

y= x/8-7/8 are two lines that are symmetric about the line

y=x