If f(x) = 2x - 3 & g(x) = x^2+5, find:If f(x) = 2x - 3 & g(x) = x^2+5, find:
a) gf(2) = g(f(2))
= g(2(2)-3)
= 2x - 3 (4 - 3)
= 2x - 12 + 9
= 2x - 3 #..........................Incorrect - see below
b) fg(-3) = f(g(-3))
= f(-3^2+5)
= 2x - 3 ( -9 + 5)
= 2x + 27 - 15
= 2x + 12 #..........................Incorrect - see below
Am I doing it correctly?
No. A composition of functions is itself a function. You feed the composition a number, and it spits out a number.If f(x) = 2x - 3 & g(x) = x^2+5, find:
a) gf(2) = g(f(2))
= g(2(2)-3)
= 2x - 3 (4 - 3)
= 2x - 12 + 9
= 2x - 3 #
b) fg(-3) = f(g(-3))
= f(-3^2+5)
= 2x - 3 ( -9 + 5)
= 2x + 27 - 15
= 2x + 12 #
Am I doing it correctly?
A quick way to know you are wrong is because g(f(2)) must be a pure number, not an expression involving x.If f(x) = 2x - 3 & g(x) = x^2+5, find:
a) gf(2) = g(f(2))
= g(2(2)-3)
= 2x - 3 (4 - 3)
= 2x - 12 + 9
= 2x - 3 #
b) fg(-3) = f(g(-3))
= f(-3^2+5)
= 2x - 3 ( -9 + 5)
= 2x + 27 - 15
= 2x + 12 #
Am I doing it correctly?