Function notation, domain and range Problem set A

\(f(x)=3x^2-5x+2\).

1. (a) Find \(f(3)\).
2. (b) Find \(f(-1)\).
3. (c) Find the values of x for which \(f(x)=2\).

Write down the largest possible domain of each function.

1. (a) \(g(x)=\dfrac{7}{x-5}\)
2. (b) \(h(x)=\sqrt{2x+6}\)
3. (c) \(k(x)=\ln(x-1)\)

Write down the range of each function, for all x in its domain.

1. (a) \(f(x)=(x-3)^2+4\)
2. (b) \(g(x)=-2x^2+8x+1\)
3. (c) \(h(x)=2^x+3\)

The graph shows \(y=f(x)\). The closed dot is at \((-1,\,-3)\) and the open dot at \((4,\,2)\). Write down the domain and the range of f.

A print shop charges \(C(n)=18+2.4n\) pounds to print n posters.

1. (a) Find \(C(25)\).
2. (b) Find the number of posters that cost £90.
3. (c) Say what \(C(0)\) means in this situation.

A ball is dropped from a platform. Its height above the ground after t seconds is \(h(t)=80-5t^2\) metres. State a reasonable domain and range for the model.

A farmer uses 60 m of fencing to make a rectangular paddock. The width is x metres, so the area is \(A(x)=x(30-x)\) square metres. State a reasonable domain and range for the model.

Find the largest possible domain of \(f(x)=\dfrac{\sqrt{x+3}}{x-1}\), and the range of \(g(x)=\dfrac{4}{x-2}\), where \(x\neq2\).

The function f is defined by \(f(x)=x^2-6x+5\) for \(0\leq x\leq8\). Find the range of f.