# Find #a# and #b# so that # f(x) = { (x^2, xle1),(ax+b,x gt 1) :} # is continuous?

##### 1 Answer

Mar 27, 2017

# a=1-b #

#### Explanation:

We have:

# f(x) = { (x^2, xle1),(ax+b,x gt 1) :} #

Both

In order for continuity at

# lim_(x rarr 1) f(x) = f(1) #

Consider the LH limit;

# lim_(x rarr 1^-) f(x) = lim_(x rarr 1^-) x^2 = 1#

And the RH limit:

# lim_(x rarr 1^+) f(x) = lim_(x rarr 1^+) ax+b =a+b#

So the requirement for continuity is:

# lim_(x rarr 1^-) f(x) = lim_(x rarr 1^+) f(x) #

# :. a+b =1 => a=1-b #