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If f(x) x2 is vertically compressed by a factor of 7 to g(x) what is the equation of g(x)?
if f(x) = x² → g(x) = ⅟₇ x² = x² / 7
What is the combinationF(x)x2 and g(x)4-x?
if f(x) = x² and g(x) = 4 - x, then: fg(x) = (4 - x)² = 16 - 8x + x2 gf(x) = 4 - x² (f+g)(x) = x² + 4 - x (f - g)(x) = x² - 4 + x (fg)(x) = 4x² - x³ (f/g)(x) = x²/4 - x (iff x ≠ 4)
Rules of differentiation?
Assume f=f(x), g=g(x)and (f^-1)(x) is the functional inverse of f(x). (f+g)'=f'+g' (f*g)'=f'*g+f*g' product rule (f(g))'=g'*f'(g) compositional rule (f/g)'=(f'*g-f*g')/(g^2) quotient rule (d/dx)(x^r)=r*x^(r-1) power rule and applies for ALL r. where g^2 is g*g not g(g)
What is the set notation for G?
The set notation for G would be written as G = {...}, where the ellipsis (...) represents the elements of the set G.
What are the example of composition?
Let f(x)=x2 Let g(x)=sin(x) f(g(x))=(sin(x))2 Which is usually written sin2 (x) g(f(x))=sin(x2 )
