Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th

# If f(x) = 2x – 1, g(x) = x+12, show that fog = gof = x - Mathematics

Sum

If f(x) = 2x – 1, g(x) = (x + 1)/(2), show that fog = gof = x

#### Solution

f(x) = 2x – 1, g(x) = (x + 1)/(2)

fog = f[g(x)]

= "f"[(x + 1)/2] - 1

= 2 [(x + 1)/2] - 1

= x + 1 – 1

= x

gof = g[f(x)]

= g(2x – 1)

= (2x - 1 + 1)/2

= (2x)/2

= x

∴  fog = gof = x

Hence it is proved.

Is there an error in this question or solution?

#### APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 1 Relations and Functions
Exercise 1.5 | Q 3 | Page 31