Question

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

Answer 1

Answer:

$f(g(x))=-30x-21$

The domain is all real numbers

Step-by-step explanation:

we have

$f(x)=-6x+3$

$g(x)=5x+4$

we know that

$(fog)(x)=f(g(x))$

In the function f(x) substitute the variable x by the function g(x)

so

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

$f(g(x))=-30x-24+3$

$f(g(x))=-30x-21$

This is a linear function (equation of a line)

The domain is all real numbers