Functions-24

If f(x)= 1/(2x + 3), then find [f (1 + h) - f(1)]/h.

Solution: f(x)= 1/(2x + 3)

=> f(1+h) = 1 / (2*(1+h) + 3) = 1 / (2+2h+3) = 1 / (5+2h)

and, f(1) = 1 / (2*1+3) = 1 / (2+3) = 1/5

So, [f (1 + h) - f(1)]/h = [1 / (5+2h) - 1/5]/h

= (5-5-2h) / {5(5+2h)h}

= -2h / {5(5+2h)h}

= -2 / {5(5+2h)}

= -2 / (25+10h)