You visited us 100 times! Enjoying our articles? Unlock Full Access!

Properties of Inverse Function

The set of va...

Question

The set of value(s) of $x$ for which $f (x) = e^{ln (- x^{2} + 5 x - 6)}$ and $g (x) = - x^{2} + 5 x - 6$ are identical functions is

[2, 3]

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

(2, 3)

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

(- \infty, 2) \cup (3, \infty)

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

R - {2, 3}

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

Open in App

Solution

The correct option is B $(2, 3)$
Given : $f (x) = e^{ln (- x^{2} + 5 x - 6)} and g (x) = - x^{2} + 5 x - 6$
For domain of $f (x)$ :
$- x^{2} + 5 x - 6 > 0$
$\Rightarrow (2 - x) (x - 3) > 0 \Rightarrow x \in (2, 3)$
and domain of $g (x) = - x^{2} + 5 x - 6$ is $R .$
and $f (x) = e^{ln (- x^{2} + 5 x - 6)} = - x^{2} + 5 x - 6$
$\Rightarrow$ Both functions will be identical if $D_{f} = D_{g}, R_{f} = R_{g}$
So, $x \in (2, 3)$

Suggest Corrections

Similar questions

x

f (x) = log (\frac{x^{2} - 5 x + 6}{x^{2} + x + 1}) + \sqrt{\frac{1}{[x^{2} - 1]}}

[.]

x

f (x) = {log}_{[x + \frac{1}{2}]} | x^{2} - 5 x + 6 |

f (x) = \frac{^{3} \sqrt{x^{2} - 5 x + 6}}{x^{2} - x - 6}

x

f (x) = log (\frac{x^{2} - 5 x + 6}{x^{2} + x + 1}) + \sqrt{\frac{1}{[x^{2} - 1]}}

[.]

A = {x, x \in Z and | x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}}

A

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program