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We have `f(x)=sin(log_(e)((sqrt(4-x^(2)))/(1-x)))` <br> We must have `4-x^(2) gt0 " and " 1-x-0` <br> `implies x^(2) lt 4 " and " x lt 1` <br> `implies -2 lt x lt 2 " and " x lt 1` <br> `implies -2 lt x lt 1` <br> Thus, domain of f(x) is `(-2,1)` <br> When x approaches to 1 from its left-hand side `(sqrt(4-x^(2)))/(1-x)` <br> approaches to infinity. <br> When x approaches to -2 from its right-hand side `(sqrt(4-x^(2)))/(1-x)` <br> approaches to zero. <br> Also, `(sqrt(4-x^(2)))/(1-x)` exists continuously for ` x in (-2,1)`. <br> Thus `0 lt (sqrt(4-x^(2)))/(1-x) lt oo` <br> `implies -oo lt "log"_(e) (sqrt(4-x^(2)))/(1-x) lt oo` <br> `implies sin("log"_(e)(sqrt(4-x^(2)))/(1-x)) in [-1 ,1]` Transcript

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00:00 - 00:59 | hello friends to in this question it is given to us that if FX = 2 Sin law root 4 - x square - 6 then the Dominos it changes means to find the function of the function so we can see what the given path is given to us to it is given to us that affects equals to sign lock busy route for minus x square upon 16 ok and we can see that this must be greater than 0 and 1 - x square is equal to zero |

01:00 - 01:59 | to from this part we can say that x square is less than 4 and we can say that X is less than one because this path should be report what is dispatched should be less than 1 and 2 x square should be less than four so from this into parts I can write -2 less than its listen to it is less than 12 does the Domino fixes for from this and this is calculated from this does the -221 this system in |

02:00 - 02:59 | this value that it now from its left inside when X approaches to 12 what will you get root 4 - x square upon 1 minus 6 and which approaches to infinity to infinity and when your ex approaches to -2 from its right side it approaches to zero then your 2 - 2 song |

03:00 - 03:59 | right side this path means effects I'm taking this this approaches towards this part approaches 20 ke so also 4 - X square + a square exist continuity for what it is country from zero to infinity because for this part it approaches to infinity and for this path it approaches to zero so that it is between 0 to infinity and again for the writers when I'm taking lock |

04:00 - 04:59 | in this equation so it can be written as like this so now teaches sign Lok root 4 - x square upon 1 minus x square to this part is belongs to now what -1 and this is by far the function and understood this is calculated lenses so |

**meaning of function**

**Modulus; signum; greatest integer and fractional part function**

**representation of function**

**Physical interpretation**

**Domain codomain and range of function**

**Graph of function: Vertical line test**

**Identity function**

**Explain Constant function with graph**

**Modulus function and properties**

**Greatest integer function and properties**