If f(x) = 2x + 3 and g(x) = x – 5, what is g ○ f?
Question
If f(x) = 2x + 3 and g(x) = x – 5, what is g ○ f?
Solution
To find the composition of the functions g(f(x)), we substitute f(x) into g(x).
Step 1: Write down the function for f(x) and g(x) f(x) = 2x + 3 g(x) = x - 5
Step 2: Substitute f(x) into g(x) g(f(x)) = g(2x + 3)
Step 3: Replace x in g(x) with the function f(x) g(f(x)) = (2x + 3) - 5
Step 4: Simplify the expression g(f(x)) = 2x + 3 - 5 g(f(x)) = 2x - 2
So, g ○ f = 2x - 2.
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