Question

Find g(f(x)) if f(x) = 2x – 3 and g(x) = x2 - 1. Please teach me.

The answer is 4x^2-12x+8

If you can teach me step by step, that would be appreciate ! I'm stuck on this question for a long time.

Answer 1

f(x) = 2x - 3; g(x) = x² - 1

g[f(x)] - subtitute 2x - 3 to g(x) instead x:

g[f(x)] = g(2x - 3) = (2x - 3)² - 1 /use (a - b)² = a² - 2ab + b²/

= (2x)² - 2·2x·3 + 3² - 1 = 4x² - 12x + 9 - 1 = 4x² - 12x + 8

Answer: g[f(x)] = 4x² - 12x + 8.