MCQ
If f(x) = ax + b and g(x) = cx + d and f{g(x)} = g{f(x)} then:
- Af(a) = g(c)
- Bf(b) = g(b)
- Cf(d) = g(b)
- Df(c) = g(a)
Solution:
Given, f(x) = ax + b and g(x) = cx + d and
Now, f{g(x)} = g{f(x)}
⇒ f{cx + d} = g{ax + b}
⇒ a(cx + d) + b = c(ax + b) + d
⇒ ad + b = cb + d
⇒ f(d) = g(b)
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A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is:
y + 1
y - 1
y
$\text{y}^2$