Question

solve these problems (in image)....answer with solution of all three

Answer 1

option a is correct i think

Answer 2

Answer:

16. Option c is correct.

17. Option a is correct.

18. Option b is correct.

Step-by-step explanation:

16.

Given Function, $f(x) =\sqrt{x-1}+\sqrt{6-x}$

To Find: Domain of the function.

Given function is not defined when x - 1  and 6 - x is less than 0.

So,

x - 1 ≥ 0

x ≥ 1

and   6 - x ≥ 0

-x ≥ -6

x ≤ 6

Thus, Domain of f(x) = [ 1 , 6 ]

Therefore, Option c is correct.

17.

Given: $\phi(x)=a^x$

To find: $(\phi(p))^3$

Consider,

$(\phi(p))^3$

$=(a^p)^3$

$=a^{p\times3}$   (using law of exponent, $(x^a)^b=x^{ab}$)

$=a^{3p}$

$=\phi(3p)$

Therefore, Option a is correct.

18.

Given: $f(x)=x^2-x^{-2}$

To find: $f(\frac{1}{x})$

Consider,

$f(\frac{1}{x})$

$=(\frac{1}{x})^2-(\frac{1}{x})^{-2}$

$=\frac{1^2}{x^2}-\frac{1^{-2}}{x^{-2}}$

$=\frac{1}{x^2}-\frac{1}{x^{-2}}$

$=\frac{1}{x^2}-x^{2}$     (using law of exponent, $x^{-a}=\frac{1}{x^a}$)

$=-(x^2-\frac{1}{x^2})$

$=-(x^2-x^{-2})$

$=-f(x)$

Therefore, Option b is correct.