Question

Let a, b and c be fixed positive real numbers. Let $f\left(x\right)=\frac{ax}{b+cx}forx\le 1.$ Then as x increases,

• A. f(x) increases
• B. f(x) decreases
• C. f(x) increases first and then decreases
• D. None of these

Answer 1

The correct option is A f(x) increases

For any increase in the value of x, increase in the numerator will be more than the increase in the denominator. This can be verified by taking a few values of x.
Simply put x = 0, f(x) = 0 and for x = 1, f(x) = $\frac{a}{b+c}$, which is grater than zero.
Hence, f(x) increase when we increase the value of x.

Alternatively:
This can be verified by plotting the graphs. The slope of the graph of the numerator will be more than the slope of the graph in the denominator. Hence, f(x) will increase.