Evaluating Functions


If f(x)=2x, f(x) = 2x, what is the value of f(4)? f(-4)?

If f(x)=ax, f(x) = ax, what is the value of a a satisfying f(1)=3? f(-1) = 3?

Two functions ff and gg satisfy the following relationships.

f(1)=2f(2)=1f(3)=2f(4)=5g(1)=3g(2)=5g(3)=7g(4)=9\begin{aligned} f(1)= 2 \\ f(2)= 1 \\ f(3)= 2 \\ f(4)= 5 \\ g(1)= 3 \\ g(2)= 5 \\ g(3)= 7 \\ g(4)= 9 \\ \end{aligned}

What is the value of (fg)(1)(f \circ g)(1) ?

Let R+\mathbb{R}^+ be the set of all positive real numbers, and let f:R+Rf:\mathbb{R}^+ \to \mathbb{R} be defined by

f(x)={1q if x=pq,0 if x is an irrational number,f(x)= \begin{cases} \frac{1}{q} & \text{ if } x= \frac{p}{q}, \\ 0 & \text{ if } x \text{ is an irrational number}, \end{cases}

where pp and qq are coprime positive integers. What is the value of f(1213)+f(π)+f(0.75)?f\left(\frac{12}{13}\right)+f(\pi)+f(0.75)?

If f(x)=2x+a, f(x) = 2x + a, what is the value of a a satisfying f(2)=2? f(2) = 2?


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