Question

How do you find ( g o h ) ( x) given g ( x ) = 2x-1 and h ( x ) = 2x²+3x ?

Answer 1

Answer:

f(x) = x – 2 ; g(x) = 3x + 5;

h(x) = 2x – 3 L.H.S.

(goh) of goh = g[h(x)]

= g(2x – 3)

= 3(2x – 3) + 5

= 6x – 9 + 5

= 6x – 4 (goh) of

= goh [f(x)]

= goh (x – 2)

= 6(x – 2) – 4

= 6x – 12 – 4

= 6x – 16 … (1) R.H.S.

go(hof) hof

= h[f(x)] = h(x- 2)

= 2(x – 2) – 3

= 2x – 4 – 3

= 2x – 7 go(hof)

= g [hof (x)] = g

g (2x – 7)

=3(2x – 7) + 5

= 6x – 21 + 5

= 6x – 16 ... (2) From (1) and (2) we get