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

Question

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

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Kennedy 5 days 2021-10-10T22:36:58+00:00 2 Answers 0

Answers ( )

    0
    2021-10-10T22:38:00+00:00

    ANSWER

    y \ne1

    EXPLANATION

    The given functions are

    f(x) = x + 1

    and

    g(x) =  \frac{1}{x}

    We want to find

    (f \times g)(x)

    We use function properties to obtain:

    (f \times g)(x) = f(x) \times g(x)

    (f \times g)(x) = (x + 1) \times  \frac{1}{x}  =  \frac{x + 1}{x}

    There is a horizontal asymptote at:

    y = 1

    Let

    y =  \frac{x + 1}{x}

    xy =  x + 1

    xy - x = 1

    x(y - 1) = 1

    x =  \frac{1}{y - 1}

    The range is

    y \ne1

    Or

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

    0
    2021-10-10T22:38:37+00:00

    f(x)=x+1 \\g(x)=\dfrac{1}{x} \\(f\cdot g)(x)=(x+1)\dfrac{1}{x} \\(f\cdot g)(x)=\underline{\dfrac{x+1}{x}} \\ \\0=\dfrac{x+1}{x} \\0=\dfrac{x}{x}+\dfrac{1}{x} \\0=1+\dfrac{1}{x} \\-1=\dfrac{1}{x} \\-x=1 \\x=1

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