Mathematics, 23.10.2019 22:20 katy3865

Which of the following is true? a. the base of a logarithmic function can be a negative number. b. a logarithmic function is the inverse of a rational function. c. the domain of the logarithmic function f(x) = log5x is all positive real numbers. d. the base of a logarithmic function can be zero.

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Answer from: pricillagarcia2002

I think the correct answer among the choices listed above is option C. The only true statement is that the domain of the logarithmic function f(x) = log5x is all positive real numbers. Hope this answers the question. Have a nice day.

Answer from: ohgeezy

Option c - The domain of the logarithmic function $f(x)=\log_5x$ is all positive real numbers.

Step-by-step explanation:

Given : Following statements.

To find : Which of the following is true?

Solution :

a. The base of a logarithmic function can be a negative number.

False, because the base of a logarithmic function is greater than 1.

b. A logarithmic function is the inverse of a rational function.

False, because the inverse of the logarithmic function is an exponential function.

c. The domain of the logarithmic function $f(x)=\log_5x$ is all positive real numbers.

True, because the domain of the logarithmic function $y=\log_bx$ is the set of positive real numbers and the range is the set of real numbers.

d. The base of a logarithmic function can be zero.

False, because the base to zero is when solved by exponent then it became 0 to the power which is always zero.

Therefore, Option c is true.

Answer from: Quest

the correct functions are

h(x) = 3x + 2

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values of k (x)

case 1) k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option 4. k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) = [2^x]-[3x + 2]=2^x-3x-> is the option 2.) k(x) = 2^x - 3x - 2

case 5) k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option 6. k(x) = 3(2^x) +2

Answer from: Quest

the answer is b.

step-by-step explanation:

identity property is where 0+whatever number=whatever number. basically 0+ a number.

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