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; ...

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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

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Range of

f (x)

(0, \infty)

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a \in R - {0, 1}

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

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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 $(0, \infty)$

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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 $(0, \infty)$