Question

Given f(x) = 2x - 1 and g(x) = x² + 5, find i)fg(x)

ii) gf(x)​

Answer 1

see explanation

Explanation:

(i)

substitute x = g(x) into f(x) , that is

f(g(x))

= f(x² + 5)

= 2(x² + 5) - 1

= 2x² + 10 - 1

= 2x² + 9

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(ii)

substitute x = f(x) into g(x) , that is

g(f(x))

= g(2x - 1)

= (2x - 1)² + 5 ← expand factor using FOIL

= 4x² - 4x + 1 + 5

= 4x² - 4x + 6