- Thread starter Jacob
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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?

a) gf(2) = g(f(2))

f(2) = 2*2 - 3 = 1

gf(2) = g(f(2)) = g(1) = 1^2 + 5 = 6

b) fg(-3) = f(g(-3))

g(-3) = (-3)^2 + 5 = 9 +5 = 14

fg(-3) = f(g(-3)) = f(14) = 2*14 - 3 = 25

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?

One obvious way to do this kind of problem is to apply the function rules from the inside out

\(\displaystyle f(2) = 2(2) - 3 = 1.\)

\(\displaystyle \therefore g(f(2)) = g(1) = 1^2 + 5 = 6.\)

Now you try the second problem and tell us what you get?

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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?

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