Question

The range of the function f(x) = 3x – 2‚ is

1 point

(a) (- ∞, ∞)

(b) R – {3}

(c) (- ∞, 0)

(d) (0, – ∞)​

Answer 1

Given : function f(x) = 3x – 2

To Find : range of the function

Solution:

f(x) = 3x – 2

This is a linear function

with no restriction /  any constraints.

The domain of a linear function is the set of all real numbers because we can substitute any real number and calculate the function value, without any constraints.

Domain =  (- ∞, ∞)

the graph of a linear function is a straight, nonvertical line that has no breakpoints.

That means that for every real number, the value of the function is well defined.

Range =  (- ∞, ∞)

range of the function f(x) = 3x – 2 is    (- ∞, ∞)

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Answer 2

The range of the function f(x) = 3x – 2 is (- ∞, ∞)

Given :

The function f(x) = 3x – 2

To find :

The range of the function f(x) = 3x – 2 is

(a) (- ∞, ∞)

(b) R – {3}

(c) (- ∞, 0)

(d) (0, – ∞)

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is f(x) = 3x – 2

Step 2 of 2 :

Find range of the function

f(x) = 3x – 2

Here f(x) is a real valued function

$\displaystyle \sf \therefore \: \: - \infty < x < \infty$

$\displaystyle \sf{ \implies } - \infty < 3x < \infty$

$\displaystyle \sf{ \implies } - \infty < 3x - 2 < \infty$

$\displaystyle \sf{ \implies } - \infty < f(x) < \infty$

$\displaystyle \sf{ \implies }f(x) \in \: ( - \infty \: , \infty )$

∴ The range of the function f(x) = 3x – 2 is (- ∞, ∞)

Hence the correct option is (a) (- ∞, ∞)

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