Figure 3 Domain and range of a function and its inverse When a function has no inverse function, it is possible to create a new function where that new function on a limited domain does have an inverse function For example, the inverse of f ( x) = x \displaystyle f\left (x\right)=\sqrt {x} fThe same applies to the vertical extent of the graph, so the domain and range include all real numbers Figure 18 For the reciprocal function f ( x) = 1 x, f ( x) = 1 x, we cannot divide by 0, so we must exclude 0 from the domain Further, 1 divided by any value can never be 0, so the range also will not include 0Domain and Range Exercises STUDYSmarter Question 1 Find the domain and range of each of the following, where y is a function of x (a) y = 5x 3 (b) y = 7x 4 (c) y = 7 (d) y = x2 (e) y = 2x2 1 (f) y = x2 2x 5 (g) y = 4 x2 (h) y = 1 2x x2 (i) y = p x 9 (j) y = p 3x 4 (k) y = p x2 4 (l) y = p 4 x2 (m) y = 1 7 x (n) y = 6 x 2 (o) y = r 1 x
Exercise 1 3 Functions Problem Questions With Answer Solution
