Question

If g(x) is the inverse of f(x) and f(x) = 4x + 12, what is g(x)?
O g(x) = 12x+4
O g(x) = 1/4x-12
O g(x) = x-3
O g(x)= 1/4x-3

Answer 1

The value of inverse of $f(x)$ is $g(x)=\frac{1}{4} x-3$.

How to find the inverse of given function?

Function, in mathematics, an expression, rule, or law that represents a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions exist ubiquitous in mathematics and are important for formulating physical connections in the sciences.

The inverse of a relationship exists as a relation conveyed by interchanging or changing the elements or coordinates of each ordered pair in the relation. Inverse relation in sets can be determined utilizing the ordered pairs. The domain and range of an inverse association can be written by swapping the domain and range of that relation.

The function f(x) is given by,

$f(x)=4x+12$

Function $g(x)$ is the inverse of $f(x)$, then:

$f(x)=4x+12$

$y=4x+12$

subtract $12$ from both sides

$y-12=4x+12-12$

$y-12=4x$

Divide both side by $4$

$x=\frac{y}{4} -\frac{12}{4}$

$x=\frac{y}{4} -3$

To find the inverse function, we exchange $x$ and $y$ in the above equation.

We get,

$y=\frac{x}{4} -3$

$g(x)=\frac{x}{4} -3$

The inverse of $f(x)$ is $g(x)=\frac{x}{4} -3$.

To learn more about the inverse function visit:

https://brainly.com/question/11735394

#SPJ9