If g(x) = (x + 1)/x,find
a) g(1) b) g(0) c) g(-1) d) g(x - 1)
To evaluate g(x) when x=k, we substitute k for x in the expression
g(k)=(k + 1)/k
or
g(k-1) = ( k-1 + 1) / (k-1)
So
1. g(1)=(1+1)/1=2
I'll leave 2 - 4 as exercise for you.
Pour your answers for a check if you wish.
a) g(1) = (1 + 1)/1 = 2/1 = 2
b) g(0) =( 0 + 1)/0 = 1/0 = ¡Þ
c) g(-1) = (-1 + 1)/-1 = 0/-1 = 0
d) g(x-1) = {(x ¨C 1) + 1}/(x ¨C 1) = x/(x ¨C 1)
(a) is correct.
For (b), you have probably indicated ∞ as the answer, although I prefer to use the term "undefined".
(c) is correct.
For (d), I suppose "¨C" is meant to be a minus sign, in which case it is correct.
To find the values of g(x), we substitute the given values of x into the function g(x):
a) To find g(1), substitute x = 1 into the function:
g(1) = (1 + 1)/1 = 2/1 = 2
b) To find g(0), substitute x = 0 into the function:
g(0) = (0 + 1)/0 = undefined. Division by 0 is not defined, so g(0) is undefined.
c) To find g(-1), substitute x = -1 into the function:
g(-1) = (-1 + 1)/-1 = 0/-1 = 0
d) To find g(x - 1), we substitute x - 1 into the function:
g(x - 1) = ((x - 1) + 1)/(x - 1) = x/x = 1
To summarize:
a) g(1) = 2
b) g(0) = undefined
c) g(-1) = 0
d) g(x - 1) = 1