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mina [271]
2 years ago
8

If f(x)=4x-16andtheDomainis{-2,-1,0,3,6},findtheRange of the function. Show all work.

Mathematics
1 answer:
Svet_ta [14]2 years ago
6 0

Answer:

R={-24,-20, -16, -4, 8}

Step-by-step explanation:

f(x)=4x-16

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

f(-2)=-8-16

f(-2)=-24

f(x)=4x-16

f(-1)=4(-1)-16

f(-1)=-4-16

f(-1)=-20

f(x)=4x-16

f(0)=4(0)-16

f(0)=0-16

f(0)=-16

f(x)=4x-16

f(3)=4(3)-16

f(3)=12-16

f(3)=-4

f(x)=4x-16

f(6)=4(6)-16

f(6)=24-16

f(6)=8

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Step-by-step explanation:

(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e., \frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}

this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>

on substituting the value x=0, we will get the value of k'(0)

{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}

(b) m(x) is a function of two functions f(x) and g(x) [ m(x)=\frac{1}{2}\times\frac{f(x)}{g(x)} ]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows : \frac{\mathrm{d} \frac{f(x)}{g(x)}}{\mathrm{d} x}=\frac{\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}}{g^{2}(x)}

this will give <em>m'(x) = \frac{1}{2}\times\frac{f'(x)g(x) - f(x)g'(x)}{g^{2}(x) }</em>

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{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}

{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }

{ NOTE : \frac{\mathrm{d} f(x)}{\mathrm{d} x}=f'(x) }

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