# Function Notation

Function notation is a fundamental concept in mathematics, serving as a concise and standardized way to represent relationships between variables and their corresponding outputs. It enables mathematicians to denote functions efficiently, using symbols that convey essential information about the function's domain, range, and operations involved. By employing function notation, mathematicians can express complex relationships succinctly, facilitating clearer communication and analysis within mathematical discourse. This notation simplifies the representation of functions, allowing for concise descriptions of mathematical operations and transformations, which are integral to various branches of mathematics, including calculus, algebra, and mathematical modeling.

- Let f(x) = 5x + 12 how do you find #f^-1(x)#?
- Given #g(x) = 5x^2 - 4x# and #h(x) = 3x + 9# how do you find g(h(x))?
- If #f(x) = 2x+1# and #g(x) = (x-1)/2#, what is #f(g(x))#?
- #f(x) = 1/x^2# for #x>=2# Then #f(x) <=# ?
- Let f(x) = 3^x-2. Find f(4) ?
- If #f(x)=x-5# and #g(x)=x^2+3#, how do you find f[g(-2)]?
- How do you evaluate the function f(x) = 1/3x + 5 at x = 6?
- Let f(x) = x - 2 and #g(x) = x^2 - 7x - 9# how do you find f(g(-1))?
- What is the inverse of #f(x)=-5x+2#?
- If f(x) = ax + b and f(2) = f(4), then what is a?
- If #f# is a group homomorphism from #S_3# into #ZZ_6#, then what is the order of #f(S_3)# ?
- If f(x)=2(x-2) and g(x)=2x-(x/3), what is f(g(3))?
- How do you find #(g*h)(4)# given #f(x)=x^2-1 and #g(x)=2x-3# and #h(x)=1-4x#?
- Given #f(x)= x^2/(x+2)# how do you find #f(-x)#?
- How do you evaluate the function with the given values of x: f(x)=8x x=3, x=1/3?
- How do you find #(fog)(12)# given #f(x)=-4x+2# and #g(x)=sqrt(x-8)#?
- Given f(x)=4x-3, g(x)=1/x and h(x)= x^2-x, how do you find h(kx)?
- Netani's hourly rate of pay is $21.80. How much does he earn for working 38 hours?
- How do you find #f(-4)# when #f(x)=8x+11#?
- How do you find x when y= -2, -1, 0 and 1 given #4(5-y)=14x+3#?