Suppose f(x)=-4x+3 and g(x)=1/x+2. Evaluate f(g(x)) and g(f(x)) for x. Note any restrictions.
Help me out guys!
2006-12-27 14:22:47 · 4 answers · asked by Veronica K 3 in Science & Mathematics ➔ Mathematics
Your restrictions would be that x cannot be 0 because g(x) includes 1/x and 1/0 is undefined.
Ok, assuming that x is not equal to 0, evaultate f(g(x)) by inserting the expression for g into f, then simplify.
Like this...
f(g(x)) = -4(1/x + 2) + 3 = -4/x - 8 + 3 = -4/x - 5
Likewise, evaluate g(f(x)) by inserting the expression for f into g, then simplify.
g(f(x)) = (1/(-4x+3)) + 2, which you could combine into a common denominator if you want.
Note that composition of functions is not usually communtative.
2006-12-27 14:31:40 · answer #1 · answered by Joni DaNerd 6 · 2⤊ 1⤋
f(g(x)) =
f(1/x + 2) (restriction: x can't be zero)
= -4(1/x +2) + 3
= -4/x - 5, x not equal to 0
g(f(x)) =
g(-4x+3) =
1/(-4x+3) + 2
The restriction here is that -4x+3 can't be zero, i.e. x can't equal 3/4. Note that x=0 is perfectly allowable here, because g(f(0)) = g(3) = 1/3 + 2 = 7/3.
2006-12-27 14:49:59 · answer #2 · answered by Anonymous · 1⤊ 0⤋
h
2006-12-27 14:53:42 · answer #3 · answered by Anonymous · 0⤊ 2⤋
purple
2006-12-27 14:26:50 · answer #4 · answered by Alex F 3 · 0⤊ 3⤋