Question

find $(n \circ m)(x)$ for the functions $m(x) = x + 3$ and $n(x) = 3x - 2$

select one:
a. $(n \circ m)(x) = 3x^2 + 7x - 6$
b. $(n \circ m)(x) = 3x - 7$
c. $(n \circ m)(x) = 3x + 7$
d. $(n \circ m)(x) = 3x + 1$

Explanation:

Step1: Define function composition

$(n \circ m)(x) = n(m(x))$

Step2: Substitute $m(x)$ into $n(x)$

Substitute $m(x)=x+3$ into $n(t)=3t-2$:
$n(m(x)) = 3(x+3) - 2$

Step3: Expand and simplify

$3(x+3)-2 = 3x + 9 - 2 = 3x + 7$

Answer:

C. $(n \circ m)(x) = 3x + 7$