Given the functions
• g(x) = x² – 3
• h(x) = x + 1
find g[ h(x) ].
—————
If g(x) = x² – 3, then
g[ h(x) ] = [ h(x) ]² – 3 <——— just replacing x with h(x)
But h(x) = x + 1, so
g[ h(x) ] = (x + 1)² – 3 <——— this is already the answer
—————
You could stop at the line above if you want. However, you can also expand that square, so the expression becomes
g[ h(x) ] = (x + 1) · (x + 1) – 3
g[ h(x) ] = (x + 1) · x + (x + 1) · 1 – 3
g[ h(x) ] = x² + 1 · x + x · 1 + 1 · 1 – 3
g[ h(x) ] = x² + x + x + 1 – 3
Now group like terms together, and you finally get:
g[ h(x) ] = x² + 2x – 2 <——— another way to express g[ h(x) ]
I hope this helps. =)
Tags: composite function polynomial quadratic linear function algebra
