Question

f(x)=x^2-3 and g(x)=2x-1, how do I find the value of g(f(3))?
Step by step please!

Answer 1

first find
\[f(3)\] and
\[f(3)=3^2-3=9-3=6\]

Answer 2

then find
\[g(6)=2\times 6-1=12-1=11\]

Answer 3

and therefore
\[g(f(3))=g(6)=11\]

Answer 4

the correct answer was 2x^2-7, I need the value please.

Answer 5

\[g(f(3))\] is not a function, it is a number. perhaps you meant
\[g(f(x))\]

Answer 6

oh yes, it was g(f(x)) i'm sorry, my mistake can you help me with that one?

Answer 7

yes we work as follows
\[g(f(x))=g(x^2-3)\] i replaced
\[f(x)\] by
\[x^2-3\] now replace the "x" in
\[g(x)\] by
\[x^2-3\] and get
\[g(x^2-3)=2\times (x^2-3)-1\] and now some algebra to finish up
\[2\times (x^2-3)-1=2x^2-6-1=2x^2-7\]

Answer 8

Oh I see now, thank you!