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Let f(x)=3x2-x+2 and g(x)=5x2-1. What is f(g(x))?
Solution:
g(x) = y\(_1\) = 5x2 - 1 ….. (1)
f(x) = y\(_2\)= 3x2 - x + 2 ….. (2)
f(g(x)) is a composite function and can be written as (fog)(x)
Where x is present in f(x) you should substitute y\(_1\)
I.e., substituting equation (1) in x which is present in equation (2)
f(g(x)) = 3 y\(_1\) 2 - y\(_1\) + 2 where y1 = 5x2 - 1
f(g(x)) = 3 (5x2 - 1)2 - (5x2 - 1) + 2
f(g(x)) = 3 (25x4 + 1 - 10x2) - 5x2 + 1 + 2
f(g(x)) = 75x4 + 3 - 30x2 - 5x2 + 3
f(g(x)) = 75x4 - 35x2 + 6
Therefore, f(g(x)) is (75x4 - 35x2 + 6).
Let f(x)=3x2-x+2 and g(x)=5x2-1. What is f(g(x))?
Summary:
Let f(x)=3x2-x+2 and g(x)=5x2-1. f(g(x)) is (75x4 - 35x2 + 6).
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