Question

find domain and range f(x)=log(4x-3)​

Answer 1

Answer:

As

f

(

x

)

=

ln

(

4

x

+

3

)

and we cannot have natural log of a negative number as also

0

, the domain is given by

4

x

+

3

>

0

or

x

>

−

3

4

.

This may also be seen by the graph of

f

(

x

)

=

ln

(

4

x

+

3

)

graph{ln(4x+3) [-10, 10, -5, 5]}

Answer 2

Answer:

Domain ∈ (3/4, ∞)

Range   ∈ (-∞, ∞)

Step-by-step explanation:

If F(x) = log N is real valued function that exists then by definition of the logN, N must be positve; i.e, N>0

$\implies N \equiv 4x-3 > 0\\\implies 4x > 3\\\implies x > \frac{3}{4} \\\implies x \in \left(\frac{3}{4} , \infty)$

Hence, Domain of the function will be all real number greater than 3/4.

The logarithmic function takes all real value.

Log N ∈ (-∞, ∞) ∀ N > 0.

For a given domain of  (3/4, ∞), range of f(x)=log(4x-3) is the set of real numbers.

Note: Remember that as the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function and vice versa, so domain and range will be reverse for function f(x) = $\frac{e^x +3}{4}$.

For more learning, you can look through these answers:

1)

https://brainly.in/textbook-solutions/q-let-b-0-b-1-express-y?source=qa-qp-match

2)

https://brainly.in/question/1259359?source=quick-results&auto-scroll=true&q=log%20domain%20expert

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