Respuesta :
Given:
[tex]g(x)=4x-6[/tex]
To find:
The function [tex]g^{-1}(x)[/tex].
Solution:
we have,
[tex]g(x)=4x-6[/tex]
Put g(x)=y.
[tex]y=4x-6[/tex]
Interchange x and y.
[tex]x=4y-6[/tex]
Isolate y.
[tex]x+6=4y[/tex]
[tex]\dfrac{x+6}{4}=y[/tex]
[tex]y=\dfrac{x+6}{4}[/tex]
Substitute [tex]y=g^{-1}(x)[/tex].
[tex]g^{-1}(x)=\dfrac{x+6}{4}[/tex]
[tex]g^{-1}(x)=\dfrac{x}{4}+\dfrac{6}{4}[/tex]
[tex]g^{-1}(x)=\dfrac{x}{4}+\dfrac{3}{2}[/tex]
Therefore, the correct option is (3).
Answer:
3
Step-by-step explanation:
y = 4x - 6
x = 4y - 6
x + 6 = 4y
y = x + 6 / 4
g -1 (x) = x/4 +6/4
= answer 3
