Question

Find all numbers at which f is not continous for the given functions. Answers must be written in interval notation.

a. g(x) = x+5/x²+6x+8

b. f(x) = (3/x²) + (2/x+4) - (x/2x-3)

c. f(x) = x/(x³-x²)

d. f(x) = [(sqrtx)+10]/x

e. f(x) = 2x/x(sqrt x+4)

f. f(x) = ln srqt(x+6/4x²-9)

g. f(x) = ln srqt(x-8/x+3)

h. f(x) = [(sqrtx)+5]/4-(sqrt x)

i. f(x) = x-1/(sqrt x²-3x+2)

j. f(t) = sin^-1 (2t-3)

Answer 1

a. $g(x) = {\frac {x+5} {x²+6x+8}}$

D: $x \in R$ / {-2, -4}

g(x) is not continuous at x є {-2, -4}

b. $g(x) = {\frac 3 {x²}}+{\frac 2 {x+4}}+{\frac x {2x-3}}$

D: $x \in R$ / {0, -4, 1.5}

g(x) is not continuous at x є {0, -4, 1.5}

c. $g(x) = {\frac x {x^{3}-x^{2}}}$

D: $x \in R$ / {0, 1}

g(x) is not continuous at x є {0, 1}

d. $g(x) = {\frac {sqrt(x)+10} x}$

D: $x \in (0,+\infty)$

g(x) is not continuous at x є $(-\infty,0]$

e. $g(x) = {\frac {2x} {x*sqrt(x+4)}}$

D: $x \in (-4,+\infty)$ / {0}

g(x) is not continuous at x є $(-\infty,-4] ∪${0}

f. f(x) = $ln {\frac {x+6} {4x^2-9}}$

D: $x \in (-6,-1.5)∪(1.5, +\infty)$

f(x) is not continuous at x є $(-\infty,-6] ∪[-1.5,1.5]$

g. f(x) = $ln{\frac {x-5} {x+3}}$

D: $x \in (-\infty,-3)∪(8,+\infty)$

f(x) is not continuous at x є $[-3,8]$

h. f(x) = ${\frac {sqrt(x+5)} {4-sqrt(x)}}$

D: $x \in (0,+\infty)$ \ {4}

f(x) is not continuous at x є $(-\infty,0] ∪${4}

i. f(x) = ${\frac {x-1} {sqrt(x^2-3x+2)}}$

D: $x \in R$ \ [1;2]

f(x) is not continuous at x є $[1,2]$

j. f(t) = $ln{\frac 1 {sin(2t-3)}}$

D: $t \in R$ \ {${\frac {2\pi n+3} 2},n \in Z$ }

f(t) is not continuous at t є {${\frac {2\pi n+3} 2},n \in Z$ }