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LenKa [72]
3 years ago
6

Let f(x) = x^2 and g(x) = 2x + 3. Write an expression that represents each composition:

Mathematics
1 answer:
rosijanka [135]3 years ago
6 0

Answer:

Remember, if f and g are functions then (f\circ g)(x)=f(g(x)), then:

a)(g\circ f)(x)=g(f(x)))=g(x^2)=2(x^2)+3=2x^2+3

b) f(f(-2))=f((-2)^2)=f(4)=4^2=16

c)

(f \circ g)(\frac{1}{x})=f(g(\frac{1}{x}))\\=f(2(\frac{1}{x})+3)\\=f(\frac{2}{x}+3)\\=(\frac{2}{x}+3)^2\\ =(\frac{2}{x})^2+2*\frac{2}{x}*3+3^2 \\ =\frac{4}{x^2}+\frac{12}{x}+9

then, (f\circ g)=\frac{4}{x^2}+\frac{12}{x}+9

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