If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?

Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

In other words, we can write this in terms of the composition of f and g as g(f(x))=x.

For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.

Now, we want to find the inverse function g(x)= that takes the value y as an input and spits out x as the output.

In other words, y=f(x) gives y as a function of x and we want to find that will give us x as a function of y.

Given,the expression y=4x+12 for y as a function of x and solve for x.

Subtract 12 from both sides we get;

y-12 = 4x+12-12

Simplify:

y-12 = 4x

Divide by 4 to both sides we get;

Simplify:

therefore,  

since, g(x) is the inverse of f(x)

⇒

Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.

Simplify:

g(f(x)) = x                for all x

⇒  g(x) is the inverse of f(x)

Therefore,

594 square inches

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