Answer:
1. Option D is correct.
2. Option B is correct.
3. Option B is correct.
Step-by-step explanation:
Inverse function defined as the the function that undergoes the action of the other function.
A function [tex]f^{-1}[/tex] is the inverse of f if whenever y =f(x) and [tex]x =f^{-1}[/tex]
To find the inverse of the function:
Q1.
Given the function: f(x) = 7x -1
Put y for f(x) and solve for x;
y= 7x -1
Add 1 both sides we get;
y + 1 = 7x
Divide both sides by 7 we get;
[tex]x = \frac{y+1}{7}[/tex]
Put [tex]f^{-1}(y)[/tex] for x;
[tex]f^{-1}(y) = \frac{y+1}{7}[/tex]
Interchange y =x, we have
[tex]f^{-1}(x) = \frac{x+1}{7}[/tex]
Q 2.
Given the function:
[tex]f(x) = x^3 - 7[/tex]
Put y for f(x) and solve for x;
[tex]y = x^3-7[/tex]
Add 7 both sides we get;
[tex]y + 7 =x^3[/tex]
taking cube root both sides we get
[tex]x =\sqrt[3]{y+7}[/tex]
Put [tex]f^{-1}(y)[/tex] for x;
[tex]f^{-1}(y) =\sqrt[3]{y+7}[/tex]
Interchange y =x, we have
[tex]f^{-1}(x) = \sqrt[3]{x+7}[/tex]
Q3 .
Given the function:
[tex]f(x) = 5x^3 - 3[/tex]
Put y for f(x) and solve for x;
[tex]y = 5x^3-3[/tex]
Add 3 both sides we get;
[tex]y + 3 =5x^3[/tex]
Divide both sides by 5 we get;
[tex]x^3 = \frac{y+3}{5}[/tex]
taking cube root both sides we get
[tex]x = \sqrt[3]{\frac{y+3}{5} }[/tex]
Put [tex]f^{-1}(y)[/tex] for x;
[tex]f^{-1}(y) = \sqrt[3]{\frac{y+3}{5} }[/tex]
Interchange y =x, we have
[tex]f^{-1}(x) = \sqrt[3]{\frac{x+3}{5} }[/tex]
