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A2 Maths C3 questions

f(x)=3-x^2 g(x)=8/3-x
a)Suggest suitable domains for the following funtion
b)Sketch the graphs in the domains you've suggested
c)Give the ranges for these functions for the domains you've suggested
d)Solve f^-1(x)=g(x)
Original post by YUANHANGCHEN
f(x)=3-x^2 g(x)=8/3-x
a)Suggest suitable domains for the following funtion
b)Sketch the graphs in the domains you've suggested
c)Give the ranges for these functions for the domains you've suggested
d)Solve f^-1(x)=g(x)


Which parts are you struggling with and what have you tried?
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Avatar for MartyO
MartyO
7
For a), are there any values of xx for which the functions are indeterminate? 83−x\frac{8}{3-x} would be indeterminate if the denominator is equal to 0.
For b), you could use a calculator to substitue values of xx to build a table of points of the functions.
For c), you could use the graphs you've made in b) to find the maximum and minimum of each function. You have to exclude horizontal asymptotes from the range.
For d), you have to find the reciproqual function of g(x)g(x), which basically means that you have to invert xx and yy in 83−x\frac{8}{3-x}, and isolate yy.
Original post by sindyscape62
Which parts are you struggling with and what have you tried?


I only knows that fx is even function and have idea about the domains
Original post by YUANHANGCHEN
I only knows that fx is even function and have idea about the domains


Think of the domain as the numbers that can go into a function without producing something undefined. For example, any function that includes x \sqrt x can't produce an output for negative numbers, so the domain is x≥0 x \geq 0 . The other main thing you can't do in a function is divide by 0, so if a value of x would mean dividing by 0 then the domain is every value except that one.

If you look at your first function there are no value of x which wouldn't work- all numbers can be squared- so the range is all real numbers. Look at the second function and see if you can identify a value that can't be put into the function.
(edited 7 years ago)
Original post by sindyscape62
Think of the domain as the numbers that can go into a function without producing something undefined. For example, any function that includes sqrtx sqrtx can't produce an output for negative numbers, so the domain is x>=0 x>=0 . The other main thing you can't do in a function is divide by 0, so if a value of x would mean dividing by 0 then the domain is every value except that one.

If you look at your first function there are no value of x which wouldn't work- all numbers can be squared- so the range is all real numbers. Look at the second function and see if you can identify a value that can't be put into the function.


So do I just put x is real number for fx then x not equal to 3 for gx
Original post by YUANHANGCHEN
So do I just put x is real number for fx then x not equal to 3 for gx


Yes that's right. The range is the possible outputs of a function- you can think about it as the possible y values when y=f(x). When you draw your graph in part b you should be able to see the range of both functions.

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