If f(x) = 2x + 3, and g(x) = x2 + x, what is g ○ f?
Question
If f(x) = 2x + 3, and g(x) = x2 + x, what is g ○ f?
Solution
To find g ○ f, we need to 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^2 + x
Step 2: Substitute f(x) into g(x) g(f(x)) = (2x + 3)^2 + (2x + 3)
Step 3: Expand the equation = 4x^2 + 12x + 9 + 2x + 3
Step 4: Simplify the equation = 4x^2 + 14x + 12
So, g ○ f = 4x^2 + 14x + 12.
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