Question

- Let f(x)= -6x + 3 and g(x) = 5x + 4. Find f•g and state its domain.

A: -30x^2 - 9x + 12; all real numbers except x = 4

B: -30x^2 - 9x + 12; all real numbers

C: -18x^2 - 39x + 20; all real numbers

D: -18x^2 - 39x + 20; all real numbers except x = 1

Answer 1

Answer:

The function is $\left(f \circ g \right) \left( x \right) = - 30 x - 21$ and the domain is all real numbers.

Step-by-step explanation:

Composition of functions is when one function is inside of another function.

The notation used for the composition of functions looks like this, $\left(f \circ g \right) \left( x \right) = f(g(x))$.

We have the following functions

$f(x)= -6x + 3\\\\g(x) = 5x + 4$

The composite function is

$\left(f \circ g \right) \left( x \right) = f \left( g \left( x \right) \right)=f \left(5 x + 4 \right) = 3 - 6 {\left(5 x + 4\right)} = - 30 x - 21$.

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

The function $\left(f \circ g \right) \left( x \right) = - 30 x - 21$ has no undefined points nor domain constraints. Therefore, the domain is $-\infty \:<x<\infty \:$ or all real numbers.