14. Determine whether x is O(g(x)) for each of these func- tions g(x). a) g(x) = x c) g(x) = x+x³ e) g(x) = 3* b) g(x) = x d) g(x) = x +xt f) g(x) = x /2 %3D %3D %3D

Q: Let f(x) = 3x – 1 and g(x) = 4 - x. Find all values of x for which f(x) < -1 or g(x) < -2.

A: Consider the function f(x)=3x-1 and g(x)=4-x. To find all values of x for which f(x)&lt;-1 or…

Q: Let f(x) = 2x – 5 and g(x) = 3 - x. Find all values of x for which f(x) 2 3 or g(x) < 0.

A: Given: fx=2x-5gx=3-x To Find:  All values of x for which fx≥3 or gx&lt;0

Q: Which function(s) has (or have) opposite end behaviours? * f(x) = x² + 3x – 1 g(x) = x³ + x? + 3x –…

A: Given, fx = x2 +3x-1  gx = x3 +x2 +3x-1 hx = x4+x3+x2+3x-1   We have to find the functions which…

Q: find the inverse of the function f(x) = 2x +3/x-4

A: Given query is to find the inverse of f(x).

Q: Find the largest interval on which f has an inverse. f(x)=1/(1+x 4)

A: Givenf(x) = 11+x4⇒y=11+x4Switch x and yx=11+y4⇒1+y4=1/x⇒y4=1/x −1⇒y=(1/x−1)1/4put…

Q: Determine h(x²) for the following function. 3x h(x) = %3D x2 + x- 6

A: Solving the problem by jus finding the value of h(x2).

Q: f(x) = x+1 x-3

A: Given:  fx=x+1x-3To prove: f(x) is 1-1 we know that, If f(x1) = f(x2) then x1 = x2 therefore f(x) is…

Q: use each set of functions to find f(g(h(x)))

A: The main objective is to find f(g(h(x))).

Q: Consider the functions: f(x) = X-4 x+5 * and g(x) = . Find the expression for the composition of…

A:

Q: Graph the function f(×)=[×] g(×)=[×]-2

A: We first  make a table for f(x)=[x]Where [-3,-2) means -3&lt;= x &lt;-2 and so on.

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.