Question

If g(x)=4x-6 then g^-1(x)=? (1) -4x+6 (2)-1/4x+1/6 (3)1/4x+3/2 (4)1/4x+6

Answer 1

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

Answer 2

Given:

$g(x)=4x-6$

To find:

The function $g^{-1}(x)$.

Solution:

we have,

$g(x)=4x-6$

Put g(x)=y.

$y=4x-6$

Interchange x and y.

$x=4y-6$

Isolate y.

$x+6=4y$

$\dfrac{x+6}{4}=y$

$y=\dfrac{x+6}{4}$

Substitute $y=g^{-1}(x)$.

$g^{-1}(x)=\dfrac{x+6}{4}$

$g^{-1}(x)=\dfrac{x}{4}+\dfrac{6}{4}$

$g^{-1}(x)=\dfrac{x}{4}+\dfrac{3}{2}$

Therefore, the correct option is (3).