Question

f: R—>R,f(x)=3^x+3^| x |= .......,Select Proper option from the given options.
(a) one-one and onto
(b) one-one but not onto
(c) many-one and onto
(d) many-one and not onto

Answer 1

Answer:

The proper option from the given options is (d), many-one and not onto.

Step-by-step explanation:

Let's show is is not onto. In fact, $3^x$ is positive for any $x \in \mathbb{R}$. So if $y<0$, there is no $x \in \mathbb{R}$ such that $f(x) = y.$ Then it is not onto.

Also, it's not one-one because

$f(-1) = \frac{1}{3}+3 = \frac{10}{3}$

and

$f(log_3(\frac{5}{3})) = 2\cdot 3^{log_3(\frac{5}{3})} = 2\cdot \frac{5}{3} = \frac{10}{3}=f(-1)$

Then the correct answer is (d)