f(x)=-3x+4 and g(x)=2x^2 -x+3 FIND (GOF)
2006-12-12 07:36:52 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(gof)(x)
= g(f(x))
= g(-3x+4)
= 2(-3x+4)^2 - (-3x+4) + 3
Simplify.
= 2(9x^2 - 24x + 16) + 3x - 4 + 3
= 18x^2 - 48x + 32 + 3x - 4 + 3
= 18x^2 - 45x + 31
2006-12-12 07:41:12 · answer #1 · answered by MsMath 7 · 0⤊ 1⤋
First, we start by defining what (g o f) actually means.
(g o f)(x) is the same as g(f(x)), so that's what you're actually solving for.
First, replace f(x) with what it's defined to be, inside the bracket.
g(f(x)) = g(-3x + 4)
Now, look at the function g(x), and replace ALL occurrences of x with [-3x + 4]. That's how functions work.
= 2[-3x+4]^2 - [-3x+4] + 3
And then now we expand by squaring the binomial and distributing the minus sign.
= 2[9x^2 - 24x + 16] + 3x - 4 + 3
= 18x^2 - 48x + 32 + 3x - 4 + 3
= 18x^2 - 45x + 31
2006-12-12 15:44:37 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
To clarify "g composed of f":
g[f(x)] = 2[f(x)]^2 - [f(x)] + 3
= 2(-3x + 4)^2 - (-3x + 4) + 3
2006-12-12 15:55:53 · answer #3 · answered by S. B. 6 · 1⤊ 0⤋
g(x)=2x^2-x+3
gof=2(-3x+4)^2-(-3x+4)+3
=2(9x^2-24x+16)+12x-4+3
=18x^2-48x+32+3x-1
=18x^2-45x+31
2006-12-12 15:42:19 · answer #4 · answered by raj 7 · 1⤊ 0⤋