FunctionHard
Question
If y = f(x)
, then
, thenOptions
A.x = f(y)
B.f(1) = 3
C.y increases with x for x < 1
D.f is a rational function of x
Solution
Given, y = f(x)
⇒ yx - y = x + 2 ⇒ x(y - 1) = y + 2
⇒
⇒ x = f(y)
Here, f(1) does not exist, so domain ∈ R - {1}
⇒ f (x) is decreasing for all x ∈ R - {1}
Also, f is rational function of x
Hence, (a) and (d) are correct options.
⇒ yx - y = x + 2 ⇒ x(y - 1) = y + 2
⇒
⇒ x = f(y) Here, f(1) does not exist, so domain ∈ R - {1}
⇒ f (x) is decreasing for all x ∈ R - {1}
Also, f is rational function of x
Hence, (a) and (d) are correct options.
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