Answer:
(f⋅g)(x) = 2x^2 + 7x.
Explanation:
To find the expression for (f⋅g)(x), we need to substitute g(x) into f(x) and simplify the resulting expression.
Given:
f(x) = 2x^2 + 3x - 5
g(x) = x + 1
Step 1: Substitute g(x) into f(x)
(f⋅g)(x) = f(g(x))
Substituting g(x) into f(x), we get:
(f⋅g)(x) = 2(g(x))^2 + 3(g(x)) - 5
Step 2: Substitute g(x) = x + 1 into the expression
(f⋅g)(x) = 2(x + 1)^2 + 3(x + 1) - 5
Step 3: Simplify the expression
Expand (x + 1)^2 using the binomial theorem:
(x + 1)^2 = x^2 + 2x + 1
Substituting this back into the expression, we have:
(f⋅g)(x) = 2(x^2 + 2x + 1) + 3(x + 1) - 5
= 2x^2 + 4x + 2 + 3x + 3 - 5
= 2x^2 + 7x
Therefore, (f⋅g)(x) = 2x^2 + 7x.