Question

dadas as funcoes f(x)=x-2 h(x)=5x g(x)=x+3 e m (x)=2x+2, calcule:
a) fog. b) gof c) goh d) hog e) gom f) mog g)fom h)mof

Answer 1

a) (fog)(x) = f(g(x))
= [g(x)] - 2
= (x+3) - 2
= x+3-2
= x+1

b) (gof)(x) = g(f(x))
= [f(x)] + 3
= (x-2) + 3
= x-2+3
= x-5

c) (goh)(x) = g(h(x))
= [h(x)] + 3
= (5x)+3
= 5x+3

d) (hog)(x) = h(g(x))
= 5[g(x)]
= 5(x+3)
= 5x+15

e) (gom)(x) = g(m(x))
= [m(x)] + 3
= (2x+2) + 3
= 2x+2+3
= 2x+5

f) (mog)(x) = m(g(x))
= 2(x+3)+2
=2x+6+2
=2x+8

g) (fom)(x) = f(m(x))
= (2x+2)-2
= 2x+2-2
= 2x+0
= 2x

h) (mof)(x) = m(f(x))
= 2(x-2) + 2
= 2x-4+2
= 2x-6