Mathematics: Let f(x) = x^2 and g(x) = 2x + 3. write an expression that represents each composition: a. (g ∘ f)(x) b. f(f(−2)) c. (f ∘ g) (1 / x)

Let f(x) = x^2 and g(x) = 2x + 3. write an expression

Ответ:

kaitlyn114433

08.01.2022

Mathematics

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

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

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

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Ответ:

hfleysher

15.06.2022

Mathematics

4/x+6

Step-by-step explanation:

qotient= division

6 more than means adding 6 to 4/x

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Let f(x) = x^2 and g(x) = 2x + 3. write an expression that represents each composition:
a. (g ∘ f)(x)
b. f(f(−2))
c. (f ∘ g) (1 / x)

Ответ:

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