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Question 1061414: f(x)=2x-3 and g(x)=x^2+2.
a) Find g(-4)
b) Show that gf(x)=4x^2-12x+11
c) Solve fg(x)=gf(x)
Answer by ikleyn(52797)   (Show Source):
You can put this solution on YOUR website! .
f(x)=2x-3 and g(x)=x^2+2.
a) Find g(-4). I sincerely hope you can substitute x= -4 into g(x)= x^2 + 2 and calculate g(-4).
b) Show that gf(x)=4x^2-12x+11. g(f(x)) = (f(x))^2 + 2 = (2x-3)^2 + 2 = 4x^2 - 12x + 11.
c) Solve fg(x) = gf(x). Hint: Calculate f(g(x)) first. Then think.
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Comment from student: Thanks i have solved the two questions!
im still stuck on the last one though, i have found fg(x) and gf(x), what would i do next?
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My response:
If you just have the expressions for fg(x) and gf(x), you have to connect these two expressions
by the sign of equality "=" and to get an equation in this way.
Then you have to solve this equation for "x".
You are on the right track !
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