Question

3x+2_81
Value of f (2) so that f(x)= 7 is continuous at x = 2 is
9* -92 is continuous
​

Answer 1

Apparently your function is not continuous at

x

=

−

3

because if you use this value you'd get a division by zero that cannot be performed.

But, if you write:

x

2

−

9

x

+

3

=

(

x

+

3

)

(

x

−

3

)

x

+

3

=

(

x

+

3

)

(

x

−

3

)

(

x

+

3

)

=

now you have:

f

(

x

)

=

x

−

3

so that now you have:

lim

x

→

−

3

x

2

−

9

x

+

3

=

lim

x

→

−

3

(

x

−

3

)

=

−

6

=

f

(

−

3

)

Your

x

=

−

3

is a discontinuity that can be removed"!

so that basically

f

(

−

3

)

=

−

6

Graphically:

graph{(x^2-9)/(x+3) [-10, 10, -5, 5]}

Answer 2

$f(x) = {3}^{x} + ^{2} - 81 \div {9}^{x} - {9}^{2} \\ \\ f(2) = {3}^{2} { + }^{2} - 81 \div {9}^{2} - {9}^{2} \\ \\ f(x) = 81 - 81 \div 81 - 81 \\ \\ 0 \div 0$