Please solve Q 2 (ii) 2 Find the domain range of the following functions - Maths - Relations and Functions

Question

Please solve Q 2 (ii)

2 Find the domain & range of the following
functions

( i i )   f ( x )   =   x   +   4   -
  3 x   -   5

Neha Sethi · Accepted Answer

Dear student fx=x+4-3x-5The domain of a function is the set of input or argument values for which function is real and defined Finding non negative values for logs and radicals:fx⇒fx≥0x+4≥0x≥-4Finding undefined singularity points:Taking the denominator of x+4-3x-5 and compare to zero Solving , x-5=0⇒x=5Combine the real ranges and undefined points for final function domain-4≤x<5 or x>5Interval Notation:[-4,5)∪5,∞Range:The set of values of the dependent variable for which a function is defined We domain : -4≤x<5 or x>5Extreme points of x+4-3x-5: now the critical points x=-4f'x=6x+4-x-132x-52x+4Put 6x+4-x-132x-52x+4=06x+4-x-13=06x+4=x+13x2+26x+169=36x+144On solving, we get x=5But x=5 is false, so no solutions for x∈R Finding undefined points of f'x=-4,x=5But x+4-3x-5 is nor defined at x=5So, x=-4So, function monotone intervals are -4

0,16∪(16,13] Note:limx→5-x+4-3x-5=limx→5-1x+4+3=15+4+3=16 Regards

Please solve Q.2 (ii) 2. Find the domain & range of the following functions. ( i i ) f ( x ) = x + 4 - 3 x - 5

Please solve Q.2 (ii)

2. Find the domain & range of the following functions.

$(i i) f (x) = \frac{\sqrt{x + 4} - 3}{x - 5}$