Find f[g(x)] if f(x) = x^2 + 1 and g(x) = x^5.

a) (x^5 + 1)2
b) (x^2 + 1)5
c) x^10 + 1
d) None of these

Question

Find f[g(x)] if f(x) = x^2 + 1 and g(x) = x^5.

a) (x^5 + 1)2
b) (x^2 + 1)5
 c) x^10 + 1
d) None of these

anonymous · Answer

@Michele_Laino @Compassionate @ganeshie8 @eliassaab

anonymous · Answer

@pooja195

michele_laino · Answer

please note that you have to evaluate this:
$$f\left( {g\left( x \right)} \right) = {\left( {g\left( x \right)} \right)^2} + 1$$
namely you have to set x = g(x) into the formula of f(x)

anonymous · Answer

so would it be (x^2+1)^5?

anonymous · Answer

then plug that back into x^2+1?

michele_laino · Answer

no, you have to solve this:
$$f\left( {g\left( x \right)} \right) = {\left( {g\left( x \right)} \right)^2} + 1 = {\left( {{x^5}} \right)^2} + 1$$

anonymous · Answer

ohh okay x^10+1?:D

michele_laino · Answer

yes! that's right!

anonymous · Answer

THANK U! :) once again amazing teacher!!!

michele_laino · Answer

Thank you! :)