Question

Let () = x + 6 and () = 5x − 2. Find the solution to the equation () = () by sketching the functions.

Answer 1

f(x) = g(x) at x=2.

Explanation:

We have, f(x) = x + 6 & g(x) = 5x - 2. Let's sketch graph step by step :

for f(x):

f(x)= x is a straight line passing through origin. Then , shift graph by 6 units in right so it be comes f(x) = x + 6 .

For g(x) :

g(x) = x is a straight line passing through origin. Then , expansion of graph by 5 units so it becomes g(x) = 5x . Then , shift the graph by 2 units to left so final equation becomes g(x) = 5x - 2.

Now, on comparing graph of both f(x) & g(x) we see that f(x) cuts g(x) at one and only point at x = 2. Also, for x = 2 , f(x) = g(x). ∴f(x) = g(x) at x=2.