A few days ago
PLZ HELP ON FUNCTIONS/INVERSE functions :(?
Ive been stuck on this for a day could someone PLEASE help?? PLEASE SHOW WORKING SO I CAN UNDERSTAND!!!
The function ‘g’ is defined by :
g : x —-> 4/(1+x^2)
a) Give a suitable domain for ‘x’ so that ‘g’ is a one-to-one function and state the range of ‘g’ for this domain.
b) Define an inverse function g^-1 stating its domain and the corresponding range.
Top 1 Answers
A few days ago
Favorite Answer
a) For x>=0, g(x) will be a one-to-one function beginning at g(0) =4, and approaching 0 as x–>infinity. For x<0, g(x) has the same value as g(-x). So the one-to-one condition is not fulfilled due to these mirror-imafe values.
So a suitable domain would be (0, +infinity) OR (-infinity, 0)
b) Let y= 4/(1+x^2); then 1+x^2 = 4/y and x^2 = 4/y - 1 = (4-y)/y, and x = sqrt[(4-y)/y].
So g^-1(x) = sqrt[(4-x)/x]
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