Question

Determine whether the function f(x)=x+1 from the set of real number to itself is one to one​

Answer 1

Let the number of appearing students be 100.

Pass only in 0 topic – 10

1 – 16 (20% of 80)

2 – 20 (25% of 80)

3 – 20% (100 – (16+20+24+20))

4 – 24%

5 – 20%

Therefore, 20% of x = 500 => x = 2500

The question is " If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?"

The total number of students is 2500.

Hence, the answer is 2500.

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Answer 2

SOLUTION

TO DETERMINE

Whether the function f(x) = x + 1 from the set of real number to itself is one to one

EVALUATION

Here the given f : R → R is defined by

f(x) = x + 1

Let x₁ , x₂ ∈ R be such that

$\sf f(x_1) = f(x_2)$

$\sf \implies x_1 + 1 = x_2 + 1$

$\sf \implies x_1 = x_2$

Thus we have

$\sf f(x_1) = f(x_2) \: \: implies \: \: x_1 = x_2$

Thus f is one to one

FINAL ANSWER

f is one to one

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