Question

If f(x) = 2x² + 3, g(x) = 5x – 2, then find

(i) fog

(ii) gof

(iii) fof

(iv) gog

Answer 1

f(x) = 2x² + 3, g(x) = 5x – 2

(i) (fog) (x) = f(g(x))

= f(5x – 2)

= 2(5x – 2)² + 3

= 2(25x² – 20x + 4) + 3

= 50x² – 40x + 11

(ii) (gof) (x) = g(f(x))

= g(2x² + 3)

= 5(2x + 3) – 2

= 10x² + 13

(iii) (fof) (x) = f(f(x))

= f(2x² + 3)

= 2(2x² + 3)² + 3

= 2(4x⁴ + 12x² + 9) + 3

= 8x⁴ + 24x² + 21

(iv) (gog) (x) = g(g(x))

= g(5x – 2)

= 5(5x – 2) – 2

= 25x – 12