Question

Solve question 8 on my attachment and show your work to get a medal.

Answer 1

\[\large{g o f (x) = g(f(x)) = (f(x))^2 + 1 = (\sqrt{x-3})^2 + 1 = x-3 + 1 = x-2}\]

Answer 2

Any doubt in this ?

Answer 3

@dianaeshun

Answer 4

Now you have to find the domain of (gof)(x) = x-2. Clearly its domain is \(\large{\mathbb{R}}\).

Answer 5

What do you mean by R

Answer 6

Real numbers

Answer 7

\(\color{blue}{\text{Originally Posted by}}\) @vishweshshrimali5
You can write it as: \[\large{x \in (-\infty, \infty)}\]
\(\color{blue}{\text{End of Quote}}\)

Answer 8

How about question 12?

Answer 9

You can write a 3 degree polynomial with zeroes a, b and c as:

\[\large{k(x-a)(x-b)(x-c)}\]

Answer 10

Here, a = -2, b = 1, c = 5

Answer 11

Thus, polynomial would be:

\[\large{y = k(x+2)(x-1)(x-5)}\]

You know this passes through (0,-3). So, x = 0 and y = -3 will satisfy it. Thus,

\[\large{-3 = k(0+2)(0-1)(0-5)}\]

Answer 12

On solving this you would find out k.

Just put it in the main equation to get the answer

Answer 13

What do you mean?