fx=x+25-x-1x2-4For fx to be real function, Quantities inside square root should be non-negative and denominator should not be 0x+25-x≥0x+2x-5≤0x--2x-5≤0Solution of x-ax-b≤0, where a 0x2-22>0x-2x+2>0x-2x--2>0Solution of x-ax-b>0, where a<b, is given by x∈-∞, a∪b, ∞x∈-∞, -2∪2, ∞But x∈-2, 5Taking intersectionx∈(2, 5]

Solve 43 sum

Solve 43 sum 42 Vhe domain Of • log I x I w R — A where A is the set (3) {2. 3.4) (4) {0. 1.2} ax The largest set of real values of x for which is a real funct. (2) (2.51 (1) (1.2) 51 0) [3.41 The domain of the function ot the

f (x) = \sqrt{(x + 2) (5 - x)} - \frac{1}{\sqrt{x^{2} - 4}} F o r f (x) t o b e r e a l f u n c t i o n, Q u a n t i t i e s i n s i d e s q u a r e r o o t s h o u l d b e n o n - n e g a t i v e a n d d e n o m i n a t o r s h o u l d n o t b e 0 (x + 2) (5 - x) \geq 0 (x + 2) (x - 5) \leq 0 (x - (- 2)) (x - 5) \leq 0 S o l u t i o n o f (x - a) (x - b) \leq 0, w h e r e a < b, i s g i v e n b y x \in [a, b] x \in [- 2, 5] A l s o, x^{2} - 4 \geq 0 a n d x^{2} - 4 \neq 0 \Rightarrow x^{2} - 4 > 0 x^{2} - 2^{2} > 0 (x - 2) (x + 2) > 0 (x - 2) (x - (- 2)) > 0 S o l u t i o n o f (x - a) (x - b) > 0, w h e r e a < b, i s g i v e n b y x \in (- \infty, a) \cup (b, \infty) x \in (- \infty, - 2) \cup (2, \infty) B u t x \in [- 2, 5] T a k i n g i n t e r s e c t i o n x \in (2, 5]

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Solve 43 sum Solve 43 sum 42 Vhe domain Of • log I x I w R — A where A is the set (3) {2. 3.4) (4) {0. 1.2} ax The largest set of real values of x for which is a real funct. (2) (2.51 (1) (1.2) 51 0) [3.41 The domain of the function ot the

Solve 43 sum

Solve 43 sum 42 Vhe domain Of • log I x I w R — A where A is the set (3) {2. 3.4) (4) {0. 1.2} ax The largest set of real values of x for which is a real funct. (2) (2.51 (1) (1.2) 51 0) [3.41 The domain of the function ot the