Given

h(r) = (1/r) + 2,find the following.
a) h(0)
b) h(-1)
c) h(-3)
d) h(x^2)
e) h(x^2 + 1)
f) h(x^2) + 1
Thank You

what's the trouble? Just plug in the value

h(r) = 1/r + 2
h(0) = 1/0 + 2 is undefined
h(-1) = 1/-1 + 2 = 1
...
h(x^2) = 1/x^2 + 2 = (1+2x^2)/x^2
h(x^2+1) = 1/(x^2+1)+2 = (2x^2 + 3)/(x^2+1)
h(x^2) + 1 = 1/x^2 + 2 + 1 =(1+3x^2)/x^2

To find the values of the function h(r) for different values of r, you need to substitute the given values into the expression (1/r) + 2.

a) To find h(0), substitute 0 into the expression:
h(0) = (1/0) + 2

Since dividing by zero is undefined, h(0) is undefined.

b) To find h(-1), substitute -1 into the expression:
h(-1) = (1/-1) + 2 = -1 + 2 = 1

c) To find h(-3), substitute -3 into the expression:
h(-3) = (1/-3) + 2

d) To find h(x^2), substitute x^2 into the expression:
h(x^2) = (1/(x^2)) + 2

e) To find h(x^2 + 2), substitute x^2 + 1 into the expression:
h(x^2 + 1) = (1/(x^2 + 1)) + 2

f) To find h(x^2) + 1, first find h(x^2) and then add 1 to the result:
h(x^2) + 1 = ((1/(x^2)) + 2) + 1

The calculations for c), d), e), and f) need more specific values or expressions to simplify further.