f(x) = x-5
g(x)= x^3
h(x)= √x^2+1

Write this expession as a composition, using only the functions f,g and h.

√ (x^3 - 5)^2 + 1

Does anyone know how to do this please? I have an exam coming up and I would appreciate it.

Question

f(x) = x-5
g(x)= x^3
h(x)= √x^2+1

Write this expession as a composition, using only the functions f,g and h.

√ (x^3 - 5)^2 + 1

Does anyone know how to do this please? I have an exam coming up and I would appreciate it.

amistre64 · Answer

the copy and paste technique tends to cut off the top of the radical.  Can you tell us what is spossed to be 'under' the radical?

amistre64 · Answer

(h o f o g)(x)  is one way to write this thing

amistre64 · Answer

h(f(x)) = sqrt. f(x)^2 + 1

f(g(x)) = g(x) - 5

g(x) = x^3

its like nesting functions; you fit them into each other like a set of russian dolls

anonymous · Answer

It is all meant to be under it. I was thinking that was the answer but I don't know how to work it out. Could you please tell me how you got the answer?

anonymous · Answer

Thank you so much for your help. I understand it a lot better now.

amistre64 · Answer

i simply used the facts they gave and tore the new equation apart to investigate its inner workings

amistre64 · Answer

we had to rip out the 'x' part and re constuct it with the missing pieces

amistre64 · Answer

sqrt. ______ ^2 +1  ; h(x) matches the profile , h(f(g(x)))
      /||||||||\

      _______ - 5  ; f(x) matches the profile, f(g(x))
     /|||||||||\

       -----   ; g(x) matches the profile

anonymous · Answer

Yeah that makes sense thanks.