Which of the following options is-are correct for exponential function f x - a x -A- Domain of f x is RB- Range of f x is 0- -C- a - R -0-1D- a -0-1 -1- -

The correct options are A Domain of f(x) is ℝ B Range of f(x) is (0,∞) D a∈(0,1)∪(1,∞) nbsp; nbsp;For f(x)=a^x to be an nbsp;exponential function, a gt; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Squaring an Inequality

Which of the ...

Question

Which of the following option(s) is/are correct for exponential function $f (x) = a^{x}$ ?

Domain of

f (x)

R

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Range of

f (x)

(0, \infty)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a \in R - {0, 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a \in (0, 1) \cup (1, \infty)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A Domain of $f (x)$ is $R$
B Range of $f (x)$ is $(0, \infty)$
D $a \in (0, 1) \cup (1, \infty)$
For $f (x) = a^{x}$ to be an exponential function,
$a > 0$ and $a \neq 1$
Clearly, domain is $R$
Since, $a > 0 \Rightarrow a^{x} > 0$
Therefore, range is $(0, \infty)$

Suggest Corrections

Similar questions

Q. The exponential function

f (x) = e^{x}

is a continuous function with domain

R

and range

Q. The domain of

f (x) = \sqrt{{log}_{x} {x}}

({x}

represents the fractional part of

x)

Q. If the function

f : R \to A given by f (x) = \frac{x^{2}}{x^{2} + 1}

is a surjection, then A =
(a) R
(b) [0, 1]
(c) [0, 1)
(d) [0, 1)

Q. Consider the real-valued function f satisfying 2 f(sin x)+ f(cos x)=x. Then, the

Q. If

e^{x} + e^{f (x)} = e,

then which among the following options are correct

Join BYJU'S Learning Program

Which of the following option(s) is/are correct for exponential function f(x)=ax ?

The correct options are A Domain of f(x) is R B Range of f(x) is (0,∞) D a∈(0,1)∪(1,∞) For f(x)=ax to be an exponential function, a>0 and a≠1 Clearly, domain is R Since, a>0⇒ax>0 Therefore, range is (0,∞)

Which of the following option(s) is/are correct for exponential function $f (x) = a^{x}$ ?

The correct options are
A Domain of $f (x)$ is $R$
B Range of $f (x)$ is $(0, \infty)$
D $a \in (0, 1) \cup (1, \infty)$
For $f (x) = a^{x}$ to be an exponential function,
$a > 0$ and $a \neq 1$
Clearly, domain is $R$
Since, $a > 0 \Rightarrow a^{x} > 0$
Therefore, range is $(0, \infty)$