FST Worksheet #2

258 days ago by mpaul

1) f(x) = 3x + 4

f(x) = 3*x + 4 show(f)

a) f(2)

f(2)

b) f(x+4)

f(x+4)

c) f(2x-1)

f(2*x-1)

d) f^{-1}(x)

var('x y') solve(x == 3*y + 4, y)

finv(x) = 1/3*x - 4/3 show(finv)

2) g(x) = x^2 - 2

g(x) = x^2-2 show(g)

a) g(-5)

g(-5)

b) g(x+1)

g(x+1)

expand(_)

c) g(-5x - 7)

g(-5*x-7)

expand(_)

d) g^{-1}(x)

solve(x == y^2 - 2, y)

ginv(x) = [-sqrt(x+2),sqrt(x+2)] show(ginv)

show(plot(g,-2,2), aspect_ratio=1)

show(plot(ginv[0],-2,2)+plot(ginv[1],-2,2))

3) f(x) = 6x + 7

g(x) = -5x - 7

h(x) = x^2 - 5

f(x) = 6*x+7 g(x) = -5*x-7 h(x) = x^2 - 5 show(f);show(g);show(h)

a) h(-5)

h(-5)

b) g \circ f(-3)

g(f(-3))

c) f \circ g(x)

f(g(x))

d) g(h(x))

g(h(x))

e) h(g(f(x)))

h(g(f(x)))

expand(_)

f) h(g(x))

h(g(x))

expand(_)

g) f^{-1}(x)

var('x y') solve(x == 6*y+7,y)

finv(x) = 1/6*x - 7/6 show(finv)

h) g^{-1}(x)

solve(x==-5*y-7,y)

ginv(x) = -1/5*x - 7/5 show(ginv)

i) h^{-1}(x)

solve(x == y^2 - 5, y)

hinv(x) = [-sqrt(x+5), sqrt(x+5)] show(hinv)

j) g^{-1}(-5)

ginv(-5)

k) h^{-1}(2)

hinv(2)

l) h^{-1}(-2)

hinv(-2)