Question

If f(x) = x2 - 1 and g(x) = 2x - 3, then (gof) (x) =?

a. (2x² + 3)
b. (3x³ + 2)
c. (2x² + 1)
d. None of these.

Answer 1

To find (gof)(x), substitute the function g(x) into the function f(x) and simplify the expression.

Step-by-step explanation:

To find (gof)(x), we need to substitute the function g(x) into the function f(x).

Given that g(x) = 2x - 3 and f(x) = x2 - 1, we substitute the expression for g(x) into the expression for f(x):

(gof)(x) = f(g(x)) = f(2x - 3)

Substituting g(x) = 2x - 3 into f(x) = x2 - 1, we get:

(gof)(x) = (2x - 3)2 - 1

Expanding and simplifying, we have:

(gof)(x) = 4x2 - 12x + 9 - 1

(gof)(x) = 4x2 - 12x + 8

Therefore, the correct answer is (d) None of these.