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Let f(x) = x + 1 and G(x)=1/x What is the range of (F*G)(X)

User Ibelka
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</p><p>f(x)=x+1 \\</p><p>g(x)=(1)/(x) \\</p><p>(f\cdot g)(x)=(x+1)(1)/(x) \\</p><p>(f\cdot g)(x)=\underline{(x+1)/(x)} \\ \\</p><p>0=(x+1)/(x) \\</p><p>0=(x)/(x)+(1)/(x) \\</p><p>0=1+(1)/(x) \\</p><p>-1=(1)/(x) \\</p><p>-x=1 \\</p><p>x=1 </p><p>

User Whallz
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7.8k points
4 votes

ANSWER


y \\e1

Step-by-step explanation

The given functions are


f(x) = x + 1

and


g(x) = (1)/(x)

We want to find


(f * g)(x)

We use function properties to obtain:


(f * g)(x) = f(x) * g(x)


(f * g)(x) = (x + 1) * (1)/(x) = (x + 1)/(x)

There is a horizontal asymptote at:


y = 1

Let


y = (x + 1)/(x)


xy = x + 1


xy - x = 1


x(y - 1) = 1


x = (1)/(y - 1)

The range is


y \\e1

Or


( - \infty ,1) \cup(1, \infty )

User Dmcnally
by
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