question on increasing function (1 Viewer)

[mathsbrain]

Can anyone provide the working for below? Tysm

 

[cossine]

Can anyone provide the working for below? Tysm

View attachment 39184

This question should be straightforward if you understand it. All it is asking is what is the domain of f(g(x)).

 

[mathsbrain]

This question should be straightforward if you understand it. All it is asking is what is the domain of f(g(x)).

What is the answer you are getting?

 

[cossine]

What is the answer you are getting?

[1, 3.5]

 

[mathsbrain]

[1, 3.5]

hmm i tried a few times still not sure how to do it, don't we find the domain of g(x) and intersect with domain of f(g(x))?

 

[cossine]

hmm i tried a few times still not sure how to do it, don't we find the domain of g(x) and intersect with domain of f(g(x))?

So you have been given the domain of g. When it say map [1, 4] to [2, 6] this means [1, 4] is the domain and [2, 6] is the range of g. Actually the question does not explicitly state the domain of g but without making that assumption the question is not doable.

 

[SadCeliac]

Where are you guys getting these random proof questions I stg I'm doing all these and everything is all normal and then I come on here and you have these wack ass questions

 

[mathsbrain]

So you have been given the domain of g. When it say map [1, 4] to [2, 6] this means [1, 4] is the domain and [2, 6] is the range of g. Actually the question does not explicitly state the domain of g but without making that assumption the question is not doable.

So we are looking for domain of f(g(x)), x values of g only makes sense if x values are within 1 to 4.
then f takes the y values of g as its x values, which means f takes values between [2,6] but domain of f is [0,5], so surely that means f takes values from 2 to 5? so I'm not sure how you are getting 3.5?

 

[cossine]

So we are looking for domain of f(g(x)), x values of g only makes sense if x values are within 1 to 4.
then f takes the y values of g as its x values, which means f takes values between [2,6] but domain of f is [0,5], so surely that means f takes values from 2 to 5? so I'm not sure how you are getting 3.5?

No, you want find {x : 0<= g(x) <= 5}. Notice x = 3.5 satisfies the condition.

#so surely that means f takes values from 2 to 5? so I'm not sure how you are getting 3.5?
This is not what the question is asking. When we consider domain we need to consider values of x not g(x).