Question

In the composition (f o g)(x), if f(x) = -10x + 15 and g(x) = 3x + 9, what is (f o g)(x)?

a) -10x + 6
b) -30x + 24
c) -30x - 6
d) -10x - 24
What is the domain of (f o g)(x)?
a) All real numbers
b) x ≠3
c) x ≠-3
d) x ≠0
In the composition (g o f)(x), what is (g o f)(x) if f(x) = -10x + 15 and g(x) = 3x + 9?
a) -30x + 24
b) -30x - 6
c) -10x - 24
d) -10x + 6
What is the domain of (g o f)(x)?
a) All real numbers
b) x * 3
c) x* -3
d) x* 0

Answer 1

To find (f o g)(x), substitute g(x) into f(x) and simplify. The domain of (f o g)(x) is all real numbers. To find (g o f)(x), substitute f(x) into g(x) and simplify. The domain of (g o f)(x) is also all real numbers.

Step-by-step explanation:

To find (f o g)(x), we need to substitute the expression for g(x) into f(x). So, (f o g)(x) = f(g(x)) = f(3x + 9) = -10(3x + 9) + 15 = -30x - 90 + 15 = -30x - 75. Therefore, the correct answer is option c) -30x - 6.

The domain of (f o g)(x) is the set of all real numbers because there are no restrictions on the values of x in the composition function.

Similarly, to find (g o f)(x), we substitute the expression for f(x) into g(x). So, (g o f)(x) = g(f(x)) = g(-10x + 15) = 3(-10x + 15) + 9 = -30x + 45 + 9 = -30x + 54. Therefore, the correct answer is option a) -30x + 24.

The domain of (g o f)(x) is the set of all real numbers because there are no restrictions on the values of x in the composition function.