Question

❣

Dᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴘᴏɪɴᴛs ᴏғ ᴄᴏɴᴛɪɴᴜɪᴛʏ ᴏғ ᴛʜᴇ ᴄᴏᴍᴘᴏsɪᴛᴇ ғᴜɴᴄᴛɪᴏɴ ʏ = ғ[ғ(x)], ɢɪᴠᴇɴ ᴛʜᴀᴛ, ғ(x) = 1/x-1.​

Answer 1

Answer:

g(x) is continuous ∀ x ∈ R-{2}

Explanation:

Let g(x) = f(f(x))

∴ g(x) is given by

$g(x)=\frac{1}{f(x)-1}$

$=>g(x)=\frac{1}{\frac{1}{x-1} -1}\\\\=>\boxed{g(x)=\frac{x-1}{2-x}}$

Now Since g(x) is a polynomial function, it is continuous at all points except at x=2.

Because at x=2; g(x) is not defined

∴ g(x) is continuous ∀ x ∈ R-{2}

Hope this asnwer helped you :)

Answer 2

Step-by-step explanation:

Answer:

g(x) is continuous ∀ x ∈ R-{2}

Explanation:

Let g(x) = f(f(x))

∴ g(x) is given by

g(x)=\frac{1}{f(x)-1}g(x)=

f(x)−1

1

\begin{lgathered}=>g(x)=\frac{1}{\frac{1}{x-1} -1}\\\\=>\boxed{g(x)=\frac{x-1}{2-x}}\end{lgathered}

=>g(x)=

x−1

1

−1

1

=>

g(x)=

2−x

x−1

Now Since g(x) is a polynomial function, it is continuous at all points except at x=2.

Because at x=2; g(x) is not defined

∴ g(x) is continuous ∀ x ∈ R-{2}

Hope this asnwer helped you :)