Let f(x) = -5x + 3 and g(x) = 6x – 2. Find f * g and its domain.
A. -30x^2 + 28x - 6; all real numbers except x = 1/3
B. -15x^2 - 8x - 12; all real numbers except x = 3/5
C. -30x^2 + 28x - 6; all real numbers**
D. -15x^2 -8x - 12; all real numbers
Algebra U2 L6 Function Operations Quick Check:
D
B
C
D
C
100%
except x = 1/3
C. -30x^2 + 28x - 6; all real numbers
f(x) = -5x + 3 and g(x) = 6x – 2.
f*g
= (-5x+3)(6x-2)
= -30x^2 + 28x - 6
the correct answer is C
don't know what the bot is going on about "except x = 1/3"
the domain is the set of reals
To find the product of two functions, f(x) and g(x), we need to multiply the two functions together.
Given:
f(x) = -5x + 3
g(x) = 6x - 2
To find f * g, we substitute g(x) into f(x) and simplify:
f * g = f(x) * g(x)
= (-5x + 3) * (6x - 2)
To multiply these binomials, we use the distributive property:
f * g = -5x * 6x - 5x * (-2) + 3 * 6x - 3 * (-2)
= -30x^2 + 10x + 18x - 6
= -30x^2 + 28x - 6
So, the product of f(x) and g(x) is -30x^2 + 28x - 6.
Now, let's determine the domain of f * g. The domain refers to the set of all real numbers for which the function is defined.
Both f(x) and g(x) are defined for all real numbers, so there are no restrictions on the domain of f * g. Therefore, the domain of f * g is all real numbers.
So, the correct answer is option C. -30x^2 + 28x - 6; all real numbers.